 Hello, this is a video about linear equations, literal equations. So literal equations are actually equations that have more than one variable in them, but you're only solving for one specific variable. So consider the Fahrenheit Celsius formula. This would be considered a literal equation because it has both F in it and C. So in the example here, the average minimum temperature for January in Juneau, Alaska is 24 degrees Fahrenheit. Let's find the temperature in degrees Celsius. So what this is telling me is that F is equal to 24. So go to your Fahrenheit Celsius formula and you plug in 24 for F. And that is equal to 9 over 5 times C plus 32. I want to find C, so let's multiply through by 5 to get rid of the fraction. Multiply by 5 or 5 over 1, however you want to do it. 5 times 24 will be 120. 5 times 9-5 is where the 5's cancel, leaving you with 9C. And then 5 times 32 would be 160. So now that they get C by itself, we do take away the 160 from both sides. We did negative 40 equals 9C. Since we're multiplying by 9, well, we should divide both sides by 9. And you're going to get about negative 40 divided by 9 is really close to negative 4. That's what C is. C is negative 4 degrees. I want you to look at the steps I did here. First thing I did was multiply by 5 to get rid of the fraction. Isolate the C by taking away the constant 160 from both sides. Then I did a division step. So we got rid of the fractions, subtracted, then we divided. Well, you know, it would be kind of rough to have to keep doing all that rearranging every time I wanted to have a Celsius temperature. So now I'm actually kind of going to come up with a generic formula that's solved for C that I can always plug directly into to find a Celsius temperature anytime I'm given a Fahrenheit temperature. So let's solve for C in the Fahrenheit Celsius formula. So the goal is to get the C term by itself and then get rid of any coefficient it has. So we're still going to start off by getting rid of the fractions. We will multiply through by 5. 5 times F is 5F. 5 times 9 over 5 leaves you just 9C plus 5 times 32 is plus 160. All right, so remember, we're trying to get the 9C by itself first. So we're going to still take away that 160 from both sides. You cannot really combine 5F and 160 into one single term you have to keep them separate. Keep them separated 5F minus 160 is equal to 9C and divide everything by nine both sides. So it turns out that 5F minus 160 all over nine is equal to C. Or if you like your variable better on the left that you're solving for C equals 5F minus 160 over 9. So this is a formula where I can plug in any Fahrenheit temperature I want. Evaluate and I can find the Celsius temperature. Always. So now we have tons of variables. We got ACX to BY. So the equation is A plus CX equals to BY. I want to solve for X. That means I need to get the CX term by itself before anything else. So we need to take this positive A here and subtract A from both sides of the equation. We will get CX equals to BY minus A. Remember the ultimate goal here we need to get X by itself. Since we're multiplying by C we will divide both sides by C. You're actually going to get a final answer of X equals to BY minus A over C. You can keep your answer in this format that is okay. How about another one? P equals D minus 2 over H minus 1. I'm going to solve this formula for H. So I think the best perch here would be to just make a proportion. I'd have P times H minus 1 is equal to D minus 2 times 1. So just D minus 2. So we need to get the H term by itself. So we should probably get the set of parentheses by itself first. So the first step that I would do would be to divide both sides by P. And get H minus 1 equals D minus 2 over P. To get H by itself now since we are subtracting 1 you add 1 to both sides. And it looks like H is equal to D minus 2 divided by P plus 1. Another formula solved for H. So a lot of this literal equation stuff is actually very useful anytime you're using formulas, especially in science where any subject matter could be business, math, anything. So I hope you enjoyed. Thank you for watching.