 The thing with the Equal Science Desk, right, I meet a lot of people that say, you know, they want equality in the world, they want sustainability in the world, they believe the world is unjust, they talk about a lot of social issues, a lot of economic issues, a lot of political issues, and all that jazz, right? But they don't really understand that what they're talking about, what the base of what it is they're talking about is mathematics, because as soon as they start talking about equality and sustainability and all that jazz, they're talking about the equal sign, right? They're talking about this symbol right here, they're saying they want equality, this side equals this side, they want sustainability, this side equals this side, right? That's what they're talking about, sustainability means, what you're taking out of the earth, you're putting at least as much back into the earth, right? Sustaining, right? They're talking about maintaining a budget, they're talking about the equal sign, right? They want to be economically independent, they're talking about the equal sign, how much you earn should be at least, right, equivalent to how much you spend, as soon as you start spending more than you earn, you're in the negative, you're not financially independent, you're in debt, right? So anyone talking about financial independence, they're really talking about the equal sign, anyone talking about the environment, sustainability, they're talking about the equal sign, anyone that's talking about social justice is really supposed to be talking about the equal sign, but unfortunately what I find is a lot of people are illiterate in the language of mathematics, so everything that they're talking about on this level has a limit to where they can take it because they don't understand that you need to quantify these things to really have that stuff in your life, right? Now for us in the last couple of streams, math streams, anyway, we talked about how to deal with addition, subtraction, multiplication and division, right? Once we learn how to do these four simple operations, and with these four simple operations, you can do almost anything you want in mathematics, right? At least in the real world, maybe not theoretical mathematics, but anything that you want to apply to your life. As long as you know how to ask, subtract, multiply and divide and move around the equal sign, right? As long as you know how to do this, you can use mathematics to do almost anything you want. So let me explain to you what it is when we say we want to move around the equal sign. So check this out. Let's say we have an expression or equation that says x is equal to 5, right? That's intuitive. That basically says whatever your x is, x is equal to 5, okay? And the units here are irrelevant. When we're talking about mathematics, just the language of mathematics, the syntax of the language of mathematics, units do not matter. This could be x, x is how many comic books I'm going to buy this week is equal to 5 comic books. So comic books be my units, right? Comic books. x could be how many cookies I've eaten, I ate yesterday and probably more than 5, but let's say 5, I'm down to 2, right? I made 2 trades. So 5 could be cookies. Okay. 5 could be a comic book that I'm buying cost $5. That could be money. It could be time in seconds, right? And time couldn't be, it's sort of a generic unit. You would have to specify, is it seconds? Is it minutes? Is it hours? Is it years, right? And different places where you apply your mathematics may use different units more often than others, right? So for example, if you're in finances, you're probably using, or you're trying to do personal finance economics, you're probably using years, not hours. You don't look at your investments on an hourly basis. If you're looking at them on an hourly basis, you're gambling, right? Minutes, gambling. Seconds, gambling, right? So the units really define where you are, where you're applying them, right? But when you're trying to learn mathematics, you don't care about the units, right? The units come into play when you're delving, when you're taking mathematics and using it in a system, right? Is it personal finance? Is it physics? Is it electrodynamics? Is it biology? Is it food? Is it shopping? Is it personal finance, investing? Whatever it is, right? So consider that when you're learning mathematics, forget about trying to apply the mathematics right away if you don't know how to syntax works, how the language of mathematics works. First, learn how the language of mathematics works, right? And it's just basically intuitive rules, and then you're going to apply the mathematics in different places, right? So for example, let's assume we didn't have x equals five. Let's assume we had this. x plus two is equal to five, right? So we take this guy out. So we say x plus two is equal to five. Well, for us, when we're trying to do mathematics, if we have an equal sign and the equal sign kicks us up into another realm, right? All of a sudden the equal sign allows us to look at different systems and try to understand different systems, right? That's the power of the equal sign. The equal sign gives us solutions to problems, right? Or questions that we have. So when you're dealing with an equal sign, if you're trying to solve something, right? Solve for x. And the x would be your unknown, okay? Slick-mic. My favorite question always used to be exponentials graphing the growth of bacteria. So yeah, I don't know why, but the correlation between inputs and outputs and systems always satisfied me. Yeah, exponentials is amazing. And it's no longer only the best example is no longer. Well, the best example is still bacteria growth or exponential decay, radioactive decay. It's also in economics right now. Or our current economic system because there's a lot of exponential growths going on. We've talked about this stuff, right? So whenever you're trying to solve an equation, right? Because this is solving for x, solving equation. The way you should think about it is your x is your unknown, right? Let's do this in blue. Let's do this in blue. Think of x is equal to unknown, right? So your unknown is what you're trying to find, right? x marks the spot. So when you're trying to solve for x, when you're trying to solve for an equation, you're trying to get the variable by itself, right? Solve for x means, means get the variable by itself, right? That's what that means. Solve for x means get the variable by itself. And by the way, some people have a hard time understanding what variable means. Okay, variable means find what the unknown is that can vary, right? Variable is something that can vary. That's it. And in mathematics, usually, preliminary mathematics anyway, we use letters of the alphabet for the unknown, for the variable. In this case, our variable is x, right? So solve for x means get the variable or get x by itself. That's what solving equation means, right? Get the variable by itself or get a specific variable by itself, right? So what do we need to do? We need to undo what's being done to it. So undo. How do you, how do you do this? How? How do you do this? How do you do this? Do you do this? The answer? Undo what's being done to x or the variable, right? So let's stay consistent. So undo what's being done to the, to the variable. The variable. In this case, for us, is x. So undo what's being done to the variable. And here is the thing. Here's a beautiful thing about mathematics. Mathematics is very unique in our lives, really, because for almost, almost everything that you can do in math, you could undo it in math, right? So in mathematics, almost always, whatever you're looking at has an opposite, right? So the opposite of addition is subtraction. The opposite of multiplication is division, right? Those are the four that we're talking about right now. The opposite of exponential powers where things are growing are radicals or roots, which are really the denominator and exponential, but we'll get into that stuff, right? And we have multiple times through the math videos, hundreds of math videos we created on the sensitive. So for us to get x by itself, we have to undo what's being done to the x to get it by itself, right? And there's an order of operations here, right? Don't forget the order of operations. Don't. Let's put a little note, note, note, note. Don't forget, oops, forget the order of operations. And what are we talking about with the order of operations? Bed mass or pet mass or depending on where you are, right? We're talking about bed mass, right? Brackets, exponents, division, multiplication, addition, subtraction, right? Now, bed mass, if you're simplifying expressions, which we just, we learned how to add, subtract, multiply, and divide, we didn't go into simplifying. We just went into straight into solving equations. Simplifying won't make sense. We'll come back to it, okay? But let's deal with the equal sign right now. So if you're simplifying expressions, you go this way. If you're solving for equations, you go the other way. Solving, right? You take your addition and subtraction first, and then multiplication, division, and then exponents, and then whatever is in the brackets, okay? In our case, we have this thing here, right? We want to solve for x and get x by itself. Well, what's being done to the x? We're adding to x, right? So to get x by itself, we have to subtract 2 from this side, right? So if we have x plus 2 is equal to 5. To get rid of this 2, we're going to subtract 2, right? Now, what does the equal sign mean? The equal sign means this. It means it's a teeter-totter, and you always have to keep it equal, balanced, and if you do something on one side, you've got to do it to the other side. That's what the equal sign means. It means this side is equal to this side. This side has to remain equal to this side. So if there's anything you're doing to this side, you have to do it to the other side, right? So for us, if we're subtracting 2 from this side, then we have to subtract 2 from this side. We have no choice. We have to keep the teeter-totter balanced. If we're adding something here, then we need to add something on this side, right? How do I put this up here? Oh my goodness, it's going to fall. Here, we'll do it this way. Here's a teeter-totter. If I add a pen on this side, I've got to add an equal pen on this side, right? It's a different color, so that's not going to work. Maybe the color weights are different. Two reds, they have to balance. If I have my teeter-totter, and if I add a pen on this side, then this side is going to go down. This side is going to go up. That's not the definition of an equal sign. The definition of an equal sign says no. If you're starting off with two things that are equal, right? Two sides that are equal, if you add something on this side, you've got to add it to this side. That's the concept, right? So if we subtract 2 from this side, we've got to subtract 2 from that side. And what do we do? We go x plus 2 minus 2. Well, positive 2 and negative 2, right? 2 minus 2, they kill each other. So what do we have left on this side? We just have x left on this side. 5 minus 2 is 3. 3. When we get to the end, we got our answer. x equals 3. We just solved for x. We solved for our unknown. We isolated the variable. Get the variable by itself. We isolated the variable. Cancellation, law of a group. Cancellation, law of a group. Does that make sense? So let's expand on this. Let's look at more complicated equations or do a couple of more samples of this, right? And we'll talk. We'll incorporate bed mass in there as well. Because bed mass, this thing here, when you try to simplify, means simplify one side if you can and simplify the other side if you can before you start moving things around or isolating the variable. And by the way, gang, thank you for the follows. Appreciate them. I'm sorry if I don't recognize them or announce them right away just because I don't want to lose a train of thought here, right? So let's do more complicated stuff, okay? And if you want to take notes by the way, gang, all you got to do is just take screenshots of this, right? And then you can just have that as a note. So let's do this. We solved for x when it's x plus 2 is equal to 5. So the question is, and this is what the question will be, solve for x. Solve for x. Now I've seen a lot of schools try to make it more exciting for kids to do mathematics. And what they do is change the x to y. Solve for y or solve for s or solve for w or solve for, I think that's fine and dandy because they're trying to get the point across that variable could be any letter, right? For me, it's ridiculous to try to change the letters to try to make it more exciting for kids to be able to solve equations or do algebra. It doesn't even have to be a letter. It doesn't even have to be a letter, right? Solve for a triangle. Solve for the triangle. Solve for the triangle. Solve for the dude. Get the dude by itself. Whatever it is, for me, it's better to add the variation in the questions based on the difficulty of the question instead of the phrasing of the question. So I like working with x because to me, x marks the spot, right? So let's do this one. x plus 7 is equal to 4, right? So we want to get x by itself. So undo what's being done to the x. What's being done to the x is 7 is being added to the x. So you subtract 7 from here. You subtract 7 up from here. 7 kills 7. Line up the equal sign. On this side, you have x by itself. 4 minus 7 is negative 3, right? Nice. Putin roster. x equals negative 3. I always like the smiley face. Solve for the smiley face. Solve for the happy dude, right? Now for me, I've mentioned this before a few times. Mathematicians are lazy, right? Especially when they're doing mathematics. For me, I like things visual and mathematicians are in general very visual, right? So when I write down x plus 7 is equal to 4, instead of writing minus 7 on this side and minus 7 on this side, I think about the adding and subtracting as movements. So I grab a positive 7, bring it over, and whenever you jump over an equal sign, the sign changes, right? So positive 7, when it goes over to the other side, becomes a negative 7. So positive 7 has moved. The only thing we have on this side is x, and 4 minus 7 is negative 3, right? Here's another one. x minus 4 is equal to 3. Well, we've got to get x by itself. This is negative 4. Borno for cities. Series. Isis. Isis. Isis. Borno, how are you doing? Welcome to another live stream. So you can think about it two ways. You can go plus 4 on this side, plus 4 on this side, so x is equal to 7, or you can think about it this way. Here, we'll do the same thing here. x minus 4 is equal to 3. I want to move the 4 plus 4, change the size. Left on this side is x, and this is 7. Up to you which one you guys want to use. I like doing this. Easy. Easy. Let's do more variations. The question is still solved for x, right? How about we do this? Are we on number 4? Let's say number 4. x plus 3 minus 4 is equal to 7 plus 2. Well, we have the equal sign here. We've got things on this side and things on that side. Now before you start solving for a variable, solving for x, isolating a variable, you did it that fast? Oh, it does too. I had to think about it. Do you stream on any other platform? I don't stream on any other platform, but I upload the videos to SensorTube. Most of the videos to SensorTube, less and less recently. SensorTube, BitShoot, and Rumble, everything goes to. So BitShoot and Rumble, I upload everything. And we upload audios when we don't have visuals to SoundCloud's podcast. Ronnie, how are you doing? Ronnie90. Hello, hello. Right? So when you're trying to solve for x, isolate the variable, I always love math to do it. Nice. Me too. Right? If you're trying to get x by itself, instead of, I mean, theoretically, you could do this. What's being done to the x here? Well, 3 is being added to x and then you're subtracting 4. So you could do it in a weird way, not a weird way, but a long way and go, okay, I'm going to grab the negative 4, bring it over. It becomes positive 4. I'm going to grab the positive 3, bring it over. It becomes negative 3 because we're jumping over the equal sign. Right? What we have left on this side is just x and this we just end up doing. 7 plus 2 is 9, plus 4 is 13, minus 3 is 10. Putin Roster got it. 10. Right? Now, that's extra work. Right? Grab everything, grab each one individually and bring them over. Right? Well, how about doing it this way? And it's faster. x plus 3, minus 4, 7 plus 2. Same question. Right? And not only is it faster, it creates less errors. Right? So whenever you're trying to solve for an equation equal sign, line up your equal sign. Really, mathematics is very visual. You want to keep everything tight, symmetrical. Keep it clean. Do you work properly? I've said this before, right? If you're going to write the word or sentence, I like apples. Right? I like apples. Right? Period. Or if you want to amplify it, I like apples. Right? That's in a sentence, my scrawny type of writing. Right? Hopefully you can read that. You don't go and say, I like apples. You don't write it like that. You could try to decipher it that way. It could be a game. Here's a puzzle. What did we say? Right? But the point of mathematics is not to make things more difficult. Right? It's to solve equations, simplify things. The point of languages is to get your point across. Right? You could use languages to create complicated puzzles, but you want to get your idea across. Right? Mano. Mano. Mano Steel 99. Hello. Hello. Twist. How are you doing? How are you doing today? Doing good. I popped a little cookie. Right? So keep that in mind. Keep your work tight. That's one of the things I try to emphasize with a lot of my students. Right? So if we're trying to isolate the ax, instead of moving these guys individually over first, what we're going to do is simplify each side as much as we can first. That's where bed mass kicks in. Right? So bed mass, if you're doing this, mass, if you're doing this, when you're simplifying, you go this way. And if you're going to simplify each side first, do brackets first. Do we have any brackets? No. Exponents? No. Division? No. Multiplication? No. Addition and subtraction? Yes, we do. Because multiplication and division have the same weight. Addition and subtraction have the same weight. It doesn't make a difference which way you do them. Okay? So we're going to do our addition and subtraction first. Well, over here, let's simplify this. Well, let's do this one first. Let's step before this one. Right? Seven plus two is nine. Cool. Three, this is positive three. Remember in the mantra, a sign in front of the number always goes with the number. So this isn't just a regular three. It's a positive three. It's not negative. And this isn't just a four. It's a negative four. Right? So positive three minus four, right, is negative one. So we've got x minus one. Right? We added one more level of doing the work to simplify at one level for us to be able to move this thing and only move one thing. Right? We're keeping track of less things. We're compartmentalizing the work. Right? On this side now, we move the negative one over, becomes positive one. We have x left and nine plus one is 10. Right? And this part is this way. We're doing solving. So when you're solving, you deal with the subtraction and addition first, and then multiplication and division, and then exponents, and then brackets. Well, in here, we had the addition subtraction. We took care of that. We ended up with the answer. We got none of the other ones. We're done. Right? Let's do more of these. We're going to build it up all the way to multiplying, dividing, and I'm not going to introduce any exponents yet, but we'll get into the brackets. Now take a look. What if we have more complicated? I have a question for you. For sure to us. What's the question before we're going to whiteboard? We've got space here. Let's do it. If it's math related, if it's not post your question and I'll do math and try to answer the question, I'm going to have a sip of tea while we wait for the question. Let's see what it's about. What I'm eating? Cookies. I'm going to pop a cookie while we wait. One more cookie. Feed your brain. How would you explain it to someone who solved that for x equals two? What do you mean? I had this issue while tutoring my niece, and I couldn't explain it to her well enough for her to grasp it in what way to a stack. So if I give you anything and she gets the wrong answer and puts down x equals two, or the answer is x equals two and you have to explain to them what that means. Yeah, let's see. Essentially you want your right hand side equals left hand side. Yeah, right hand side equals left hand side. So you had x plus three. Okay, sure. Let me write that down. x plus three minus four. So we have x plus three minus four is equal to seven plus two. x plus three minus four is equal to seven plus two. So the way we did it when x minus one is equal to nine, grab the one over plus one. So x is equal to ten. So she ends up doing it and she gets x is equal to two. Your niece probably does not understand the x. So for this she would do the work and get x equals two. And you want to explain to her why that's wrong? Roddy says this, I never liked the whole left hand side, right hand side. The position of those numbers can be anywhere and the x would be solved fine. Sure, but every line when you're solving for something, every line is equivalent to the previous line. So this line and this line are the same line and the same line. So all of these are the same, right? I just woke up, but I see where she messed up. She did on both sides. Yeah, I was, I'm assuming where she messed up was when she did this, she would have added this thought that this was seven, right? So she would have done this and then the seven would have killed the seven. So x plus seven is equal to seven plus two. She would have misread this thing as a negative, put a seven and then brought this guy over minus seven and then you get seven kills seven. So you get two. If she did that, right? And that's the one thing. It's extremely important, it's extremely important to be able to see students work as someone as an educator, right? That's one of the reasons centralized education is so horrendous because a lot of it has to do with what do you call it? Yes and no or fill in the blanks or what do you call it? Multiple choice questions, right? So the only feedback a student can ever get is wrong or right, right? And the educator in general is not going to be looking at the students work because all they do is they hand in their multiple choice little sheet thing they scan, right? So there is no construct of feedback to students, which is just one of the reasons centralized education is just so horrendous. Okay. I haven't done simple math in years. My last math class was calculus three, so she threw me for them. Yeah. Teaching, look gang, trying to teach simple mathematics, just the basics of mathematics up is a difficult thing to do. Okay. Sometimes more difficult than the more complicated stuff, because the more complicated stuff the person you're talking to has a rudimentary understanding of the language of mathematics. When you're trying to build it from the base up, there is no conceptual understanding of the language of mathematics. So it becomes difficult. It requires patience, right? I have to look at it a little closer. Yeah. I hope that works, right? So if we're going to get into more complicated stuff, right? Here. X minus three plus two minus one plus four is equal to seven plus seven minus two, right? You could do any adding and subtracting in here, right? What do we have? Four, five. This is number six. Line up your equal sign. Combine like terms here. Seven plus seven is 14. Minus two is 12. Negative three. And you can, you can, what you can do is combine things. We got 10 already. I haven't done it yet. We got 10 again now. So what you can do is, instead of doing all the operations in one go, if you notice the pattern, you got 14. Oh, somebody's wrong. If you, if you notice a pattern, you can start eliminating things, simplifying things. So take a look at this thing. You got negative three and negative one. So minus three and minus one, you can think of as negative three and negative one. Well, negative three minus one is negative four plus four is zero. The negative four and four kill each other, right? So this, this and this are gone. You got a two left, right? Now you could write this here or you could have done the simplification here and did, brought it over here, right? I'm just going to do it over here instead of doing it here. So you see how it works instead of combining multiple operations in one shot, right? Okay. So we got x plus two here and then bring that over. You got this, you got x equals 10 and that's your answer, right? Student, why do numbers kill each other? They're a war. They cancel each other out. I know. I say kill. Maybe I should be saying cancel, but shorter word, less, less letters when we have null. And by the way, this may touch on Graham's question. What was it called? Public something. But I do almost anything to teach kids mathematics, right? And I found where you say negative three and negative one kill four. When you say they kill each other, kids tend to like that more than cancel each other out. So I have students that sometimes they're not really paying attention and they're not into it. They like it when we start killing numbers. So they pay attention and learn the process. Even though the word killing is not the best thing to use, it's a means to teach mathematics. I'm okay with that. Okay. So that's how we deal with adding and subtracting, right? Let's look at multiplication. Let's do something like this. Let's do two X is equal to eight, right? Roast of poon. As soon as I wrote it down, I knew you knew what that was, right? So whenever you have a number in front of a variable, a number in front of an X, right? That means multiplication. So this really means, this really means two times X, but we're not going to, mathematicians are lazy. We're not going to include that, right? So, so is the police. We should tell the students getting an A means you killed the cars, maybe. Well, we do have something like that. You know, when in sports you do, they say, oh, he killed it, or they killed it, right? Or musicians, oh man, they want on stage, they're set. Just, they just killed it, right? It is used. I would be the kind of kid who pays more attention, kind of kid who pays more attention if you kill numbers, yeah. So equals is the police equality. Hi, I'm Chico by the way. Das, 89, how are you doing? So over here, this is multiplication, right? Two times X is equal to eight. Well, it's the opposite of multiplication. What's the opposite of multiplication? Division. So to get X by itself, right, divide this side by two, and the equal sign says if you do something on one side, you got to do it to the other side, you divide this side by two, line up your equal sign, two kills two, you got X on this side, eight divided by two is four, right? So what did we do? We didn't have any addition, subtraction to deal with, so we just went into multiplication and division and dealt with that, right? Easy, peasy. Okay, let's do some more examples. That was number seven. Let's do number eight. Good, thank you. Cleaning the inside of my gaming console while watching you. How are you doing? Good, thank you. Eating cookies, doing mathematics, life is sweet. And cleaning the console, which console? Which console are you having to clean the console forever? Man, I think last time I cleaned the console was probably a Sega system or NES, NES probably, NES. Or N64, N64 is probably the last time I cleaned the console, N64 for sure, N64. So what if we had the following, right? X over two is equal to eight. Well, this means division, right? X divided by two is equal to eight. What's the opposite of division? Gaming computer, not my console. Oh, gaming computer, okay. My computer I cleaned like last year. Man, was it ever dirty? Yikes, I loaded up pictures. I would not try that, afraid of bronking it. X equals 16. Did you get it? Yeah, computer, you need to clean every now and then. So the opposite of division is multiplication. So we multiply this side by two, equal sign, line it up. And if you do something on one side, you got to do it to the other side. Eight times two is 16. Putin roaster got it. And when you're multiplying fractions, right, X over two times two, that's just two over one. Anything from the top can kill anything from the bottom. Two kills two, you got X left over. The other way you can think about this is this. X over two times two, this equals two X over two, and the twos kill each other, right? But I'm just killing the fractions, right? I'm breaking it, sorry. I'm French, so I sometimes make English with no worries. Bronking it, I want bronking it. That's a good word for breaking it too. So that makes sense, right? Easy? Well, let's do one that's a little bit more complicated. What if we had two X plus five is equal to eight? Huh? Well, are we solving or simplifying? Do we have any simplifying to do on this side? We can't combine two X and five. It just doesn't work, right? This doesn't have an X. And this has a variable. 1.5 you got? It is 1.5. Here's an eight, right? So if we're solving, there's no simplifying to do here. If we're solving, we do subtraction addition first. We can't add or subtract. There's nothing to add and subtract here. And then we deal, oh, sorry. If we're solving, we got an addition here we've got to deal with, right? So simplifying, we're going this way. Solving, we're going this way. So we're going to grab this guy and bring it over. So we're dealing with subtraction addition first. This becomes minus five. Eight minus five is three. Over here, we've got two X. Now what we've got to do is deal with the multiplication division. And we've got a multiplication. So divide by two, divide by two. So X is equal to three over two, which is 1.5 as Putnam Roaster says, right? Let's do a couple more, which were more complicated. Okay. That was number nine. Let's do number 10. Number 10. Let's go two X plus five minus three plus four X is equal to eight plus two. Much longer. I sort of start off simple and I kick things up to harders first. Mine CC. How were you doing? Welcome to our live stream. Putnext. Did you figure it out yet? So do the simplifying first. Either side four over three. Cool. You're a double checker. Make sure you're making sure we do it right. So you're going to simplify each side first. Brackets. So you're going to simplify this side, simplify that side. Line up your equal side. Brackets, exponents. No. We've got division multiplication. No. We've got addition subtractions. Yep. Eight plus two is 10. And then we got two X plus four X. Combine your like terms, right? Two X plus four X is six and then you got positive five minus three. That becomes positive two. Right? So we took care of simplifying each side first. There's nothing else to simplify here. Nothing to simplify here. We go into solving. We go this way. Take care of addition subtraction first. Well, there's an addition here. Let's move it over. It becomes minus. Eight minus two is eight. Oh, sorry. 10 minus two is eight and we've got six X left left here. No more adding subtracting. Then we've got division multiplication. Divide this side by six. Divide this side by six. So X is equal to eight over six, but you can simplify that because two goes into both of them. So let me write down eight over six and let's do this over here. We've done a lot of videos on these. I haven't done it in this live stream in this order first because I wanted to get into the equal sign right away. But do this. Eight. Breakdown eight into prime factors. Two times four, two times two. Six. Breakdown six into prime factors. Two times three. So this equation is really eight over six is really two times two times two divided by two times three. And anything divided by itself, they kill each other. So this is a multiplication between all these. So two kills two. Nothing else simplifies. So two times two is four. And then the bottom, you got a three. So it's four over three. That's a long way of doing that. Once you do two or three of these, then you know the rest. The flow is it is. So four over three. We've got double confirmation. Mine C. So let's do more complicated. Let's add a bracket in there. Let's add a bracket in there. Two, three X minus one is equal to four plus seven. Okay. So what are we going to do? We're going to simplify first, right? Because we can. We can simplify this side. We can simplify this side. So we're going to deal with brackets first. Do we have brackets? Yes, we do. What does a number in front of brackets mean? It means the number in front multiplies. And did you do it already? Speedy Gonzales. So the two multiplies here and multiplies here. Line up your equal side. So two times three X is six X. Two times negative one is negative two. So we have no more brackets. No brackets there. Exponents. No division multiplication. No. We got addition, subtraction. Yep. Four plus seven is 11. Cool. We got nothing else. No simplifying to do. So we're going to solve for it. We're going to go into solving. So we finished the simplifying. We came all the way to here and now we're going to go into solving, right? So we came to simplifying and now we're going into solving. Okay. Solving, we're going to deal with addition and subtraction. Oh, we got a subtraction. Bring it over becomes addition. So you got 13 on this side. On this side, you got six X. Oh, Putin next. Did you do? Oh, you did it wrong at first. Oh, that's where speed gets here. Speed kills you. Right. So now we're going to get X by itself. This is six times X. So divide by six is 13 over six. And this doesn't simplify anymore. Right. Speed kills. Okay. Easy. Easy. Right. Undo what's being done to the X. What's being done to the X? It's being multiplied by three. One is being subtracted while the whole thing is being multiplied by two. Well, if we're going to undo what's being done to it, we have to go with solving, right? Or sorry, we did simplifying first. And then we're down to here. Undo what's being done. You do the solving. You get the chess. Right. Mind see, memorize multiplication table is the most difficult thing. Is it? Multiplication table should be easy to memorize because there's a pattern to it. You don't have to know the whole table. You just have to know half the table and that half the table you just generate. You generate enough, you know the words. Like, did you have to memorize the alphabet? Yeah. At some point, we memorized A, B, C, D, E, F, G, H, I, J, K, L, N, O, P, Q, R, S, D, U, V, W, X, Y, Z. Right. At some point, we had to memorize it. But once you end up using it a lot, it's just part of your dialogue. Right. It's difficult after 12. It's difficult. I don't memorize after 12. I just do. Well, more so, more so. Who came up with the ordering of alphabet? I don't know. My guess would be linguists. Right. My guess would be linguists. So let's do one more. Okay. What number was that? 10? 11? Let's do number 11. What are we going to add? Well, let's do this. I'm going to make it more difficult. We're going to take a huge step forward. Right. So number 11, 2. X minus 1 divided by 5 plus 3. Let's go minus, minus 3 times 2X plus 4 is equal to 4X minus 1. All of it divided by 2. And I'm doing this because I want to show you the rhythm of this. Right. Now, this is more difficult than what we should be able to do. I wouldn't usually kick it up to this level, but I want to just end this section with this and then get into the chat and see if we want to go anywhere else with this. Right. So there's a rhythm in this. Right. You could deal with the brackets first if you want. Or whenever I see this personally, when I see fractions, I multiply the whole equation by the common denominator, which I haven't shown you guys this in this math session, but we've done a lot of this stuff previously in the previous math videos we've done. Right. Multiply the whole equation by the common denominator. The common denominator is 10. What's the common denominator between 5 and 2? 10. So you multiply everything by 10. All the terms, there's three terms here. One term, two terms, three terms. So 10 multiplies this, multiplies this, multiplies this. Putnar. Did you get it? Did you get a twist? Let's check it out. So the reason we're going to multiply by 10 is because the denominator dies. The 10 kills the 2. Right. 2 goes into 10 five times 5 now multiplies the top. This side. Check and look at this thing. I'm going to do this thing on the side. So 4x minus 1 divided by 2 times 10. That's 10 over 1. 2 goes into 10 five times, so it's really just 5 multiplying this and that. So this becomes 20x minus 5. Okay. Twist. You say negative 119 over 76. Let's check it out. Over here, 10 multiplies this. It becomes 30 times 2x plus 4. The 10 doesn't multiply the inside because this is one term. It just multiplies what's on the outside of the bracket. Okay. Let me make this so it looks better. This one, 2 bracket x minus 1 times 5. The 5 knocks the 10 down to 2, so it's just 2 multiplying this. So this becomes 4 on the outside x minus 1. Now we've got more simplifying to do. We're going to deal with the brackets first. Line up your equals sign. 4 multiplies in, negative 30 multiplies in. So this is 4x minus 4 minus 60x minus 120. This is 20x minus 5. We're still in the simplifying phase. We're going to simplify each side first. Line up your equals sign. Combine your like terms. Okay. 4x minus 60x is negative 56x. Negative 4 minus 120 is negative 124. We've got 20x minus 5. Now when you're trying to solve for x, it means you need to get all the x's to one side and have the result being x equals something. Right? Well, we have x's on this side. We've got x's on this side and we've got a number on this side and a number on this side. So what I'm going to do is I'm going to grab this 20x. Bring it over. It becomes minus 20x. I'm going to grab this negative 124. Bring it over. It becomes plus 124. Line up your equals sign. Negative 56x minus 20x is negative 76x. Negative 76x. 124 minus 5 is 119. Right? Twist. You got it correct. Very good. My seat says I'm slow. That's okay. That's okay. This is not about speed, by the way. Right? That's one of the other reasons centralized education is so horrendous. They put people under the clock. Get it done. Get it done. Get it done fast. Well then, why are you speeding things up? The first thing they teach you when you learn how to drive is speed kills. Well, if speed is so dangerous that it kills, why aren't they forcing students to react rapidly? Crazy. Right? I do mine quite differently. Do you? I use fractions the whole way. Use fractions the whole way. Cool. I don't like memorizing or doing quickly. I prefer intuition. Yeah. You sacrifice accuracy for the sake of speed. You sacrifice accuracy for the sake of speed, which is, well, speed kills. Right? And then you divide by negative 76. You divide by negative 76. So x is equal to negative 119 over 76. And that is your answer. And honestly, gang, if you're doing mathematics in school, when you're doing problems, when you get to the end, circle your answer, your teacher will thank you for it. Your markers will thank you for it. That way they don't have to decipher your hyaloglyphics to find out what the answer is. They automatically see it and makes their job easier, make their job easier. And gang, thank you for the follows. Appreciate the support. That's basically sort of an intro to solving for x, dealing with the equal side.