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### Course: Algebra (all content)>Unit 2

Lesson 12: Old school equations with Sal

# Solving an equation for a variable

The perimeter of a rectangle is equal to 2 times the length plus 2 times the width. We can solve for the length by isolating it on one side of the equation. We do this by subtracting 2 times the width from both sides, and then dividing both sides by 2. This gives us the formula for the length. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• How would you solve this?

-2(a+b)+5=x

Thanks guys :)
• First, you would multiply the parentheses by the outside #. This is using the distributive property.
-2(a+b)= -2a-2b
The problem now looks like this.
-2a-2b+5=x
This equation cannot be simplified anymore because the variables of a,b, and x are unknown. Hope this helped. =)
• Where do we start when we have the problem A/B=C when we are trying to solve for B
• A good way to start would be to get the B "on top" of a fraction, rather than on the bottom. In this case, you can do that by multiplying both sides of the equation by B. This gives you A = BC.

Now we need to get rid of the C which is currently on the same side of the equation as B. We can do this by dividing both sides of the equation by C. This gives you A/C = B. And so we have solved for B: we have B = A/C.
• Wouldn't the 2 cancel with 2w?
• I was going to ask the same thing but I realized that doing so will effect the outcome of P.
Doing this will leave P alone. Just like Andrew said, p/2 -w would be the answer.
• is there such a video called "What is a variable?"
• Yes, there is! In fact, one right here in the website under Algebra I. Just use the search bar and type: "What is a variable." You should be able to find it.
• How about if you have a word problem like, "A train makes a trip at 65 mi/h. A plane traveling 130 mi/h makes the same trip in 3 fewer hours. Write and solve an equation to find the distance of the trip."
I have this word problem for math homework and I tried solving it with the equation "65mi/h=130mi/h-3" but for some reason I keep on getting the wrong answer. Any help with this problem would be greatly appreciated! Thanks in advance! :)
• The key phrase is "makes the same trip". This means both the car and the plane covered the same distance. So, your equation needs to be based upon:
`distance of car = distance of plane`

Distance is calculated as Rate * Time.
You were given the rates: car = 65mph; plane = 130mph.
For time, you can use: h=car's time and h-3=plane's time.
Thus...
Car's distance = 65*h
Plane's distance = 130(h-3).

The equation becomes:`65h = 130(h-3)`

Once you solve for "h", you can find the distance by doing 65*h.

Hope this helps.
• how would you 'un'-isolate a variable exactly? can i get some help?
• What do you mean by "un"-isolating a variable?
(1 vote)
• Am I the only person who is getting problems like "− 5p + 7q − 7r + 2 = 2q − 9r − 6" on the problem set for this video which is only covering a single very simple problem?
• I think the perimeter of a rectangle is P = 2(w+l) and I think it it much easier to use than the other one. Is this true?
• what if the only coefficient is 1 and all the other #s on the left hand side are variables but on the right side it's like 67 + 93
(1 vote)
• If the variables were the same variable, add them and 67 + 93, for example:
67 + 93 = 2x + 8x
160 = 10x
Isolate x, divide both sides by 10.
16 = x
If the variables are different, it depends which variable you were solving for. Say you were solving for x.
67 + 93 = 4x + 3y
160 = 4x + 3y
Subtract 3y by both sides.
160 - 3y = 4x
Divide both sides by 4.
40 - 3y/4 = x
• How would I solve this equation?

x + 3y = 9

## Video transcript

Solve P equals 2l plus 2w for l. So this right here, this is just the formula for the perimeter of a rectangle. Perimeter is equal to 2 times the length plus 2 times the width. But they just want us to solve this equation right here, solve for l. So let's do that. So we have P is equal to 2 times l plus 2 times w. So we need to solve for l. So let's isolate all of the l terms on one side. And the best way, we could just do that by leaving it here on the right and then getting rid of this 2w. And the best way to get rid of this 2w is to subtract it from the right. But if you're going to subtract it from the right, you also have to subtract it from the left if you want this equality to hold. So you have to also subtract it from the left. And so the left-hand side becomes P minus 2w. And the right-hand side, you get-- this 2w minus 2w cancels out. You just have a 2l. And then if you want to solve for l, you just have to divide both sides of this equation by 2. You just divide both sides of this equation by 2. And we have isolated our l. We get l is equal to P minus 2w over 2. Or if we wanted to write it the other way, you could write l is equal to P minus 2w over 2. And we are done.