 In this video, I'm going to do one additional example of graphing linear inequalities. Sometimes the equations, some of them will be set up in slope intercept form, some of them will be set up in standard form, and then others will look like this. This little inequality here, we got parentheses, we got all sorts of different stuff. This isn't standard form, this isn't slope intercept, it's just something a little bit different. Basically what this problem involves is we have to simplify first a little bit, get the inequality to what we want it to look like, and then we need to graph it. So I just want to do an example of this. I'm going to go a little bit faster this because I want this to be a quick video, but you can always rewind or fast forward if you know certain parts and want to see something again. Okay, so the first thing I'm going to do is I'm going to get this in a form that I like. I want this to look like y equals mx plus b. I like to graph in this form, so I want to get y by itself. No, we're treating this like an equal sign, kind of so we're treating this like an equal sign, so I'm going to add and subtract, multiply, divide across this just like you would a normal equal sign. Okay, first thing I'm going to do is I'm going to take this three fourths and distribute it into the parentheses, think of it this way, three times eight divided by four. That's a division bar, fraction bar, however you want to think of it, but it still means divided by four. Three times eight, which is 24, 24 divided by four is six, that would be six x. Okay, so I'm going to do the same thing with two, three times two, I'll just put the negative in there first, three times two is six, six divided by four is going to be, hold on, six fourths, which reduces to three halves. Okay, I wanted to put the three halves in there, not the six fourths. So I did a little bit of what I call chicken scratch off here on the side. Okay, so it is greater than six. So I distributed the three fourths into the parentheses and got this. So my goal is again to get the y by itself. All right, so to get y by itself, this six x needs to move to the other side. So I'm going to subtract six x over to the other side. Okay, subtract six x over to the other side. And then now this will get a little tricky. I'm going to multiply everything times negative two thirds. I'm going to multiply everything times negative two thirds. So actually I'm going to show this, this is kind of a tricky step here. So I'm going to show this step. Everything is going to get multiplied by negative two thirds. Notice it's reciprocal of what we have here. If I take negative two thirds times this over here, everything's going to cancel, I'm going to be left with one. So this is going to be one y here. Okay, so this is going to be one y here. That's what I want. Okay, now I'll deal with this inequality here in a second. Okay, now what I'm going to do is I'm going to take this and multiply in here. Let's deal with the negative first. Negative times negative is a positive. All right, so now I've got two times six, which is 12. 12 divided by three is four. So this is going to be a four x right here. All right, and actually that's kind of nice because right here six and six. So the numbers are going to be the same. It's just the signs that are going to be different. Two times six is 12 divided by three is four. And it's a negative four because when I multiply in here it's negative. All right, so that's the right side. That's the right side of the equation. Now notice here that this inequality, I saved this for last. One rule that you need to remember when dealing with inequalities. If you multiply or divide by a negative number, you must flip the inequality. If you multiply or divide by a negative number, you need to flip the inequality here. Okay, that's why I saved that for last. It's a very important point. A lot of students forget that. It's a tricky little rule that's not remembered very easily. So anyway, if you multiply or divide by a negative number, flip the inequality. Okay, so now I've met my goal. I now have something that looks like slope intercept form. I got y finally by itself. Now I need to draw my boundary first. So I'm going to draw that as if it's an equation. So I got a y intercept of negative four, which is all the way down here. Okay, now if you don't know how to graph in slope intercept form, I suggest you go watch my previous video about graphing lines in slope intercept form. But anyway, a y intercept of negative four, which is down here, and I have a slope of four over one. So I'm going to rise one, two, three, four and run one in the positive direction, one, two, three, four and one. There we go. All right, so those are my points for my boundary. This is a less than, so it's going to be a dashed boundary. So here, here, there we go. Sorry about the screeches from the pen there. Okay, now that I have my boundary, now I need to figure out do I need to shade. Now this looks like I have to shade left or shade right, but that's not what we're doing here. We're not shading left or right, we're shading up or we're shading down. There's no left and right here, it's just up and down. We don't shade left and right, we shade up and down. So now I'm going to come back to my equation over here. The y's are less than the line. I used this to create the line, so I'm going to treat this as the line. The y's that I want, the y's that I'm going to shade are less than this line. So here's the line, the y's that I want are less than this line. Less than is down. So this is the portion in which I want to shade right here. There we are. Okay, that is one additional problem about graphing linear inequalities. That one is a little bit more difficult of a problem because we had to do some simplifying first and it had to remind you about multiplying or dividing by a negative flips that inequality. Then we had to graph the boundary and then we had to figure out, okay, the y's are less than. The y's are less than, we go down and this is where the shading happens. Okay, hopefully this video was informative. Hopefully this will help you graph linear inequalities. Thank you for watching.