If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Intro to equations with variables on both sides

Worked example: Learn to solve the equation 2x + 3 = 5x - 2.  Created by Sal Khan.

## Want to join the conversation?

• Hi, I had a math test few days ago and didn't get one question. Can anyone tell me the answer and steps to solve it?
The question is: 3(1-2x) = 4-6x Thank You. •   Isaac,
3(1-2x) = 4-6x First distribute the 3
3*1 - 3*2x = 4-6x And multiply the terms
3-6x = 4-6x Then add 6x to both sides.
3-6x+6x = 4-6x+6x The -6x+6x becomes zero
3-0 = 4-0 And subtract the 0 from each sides
3=4
3 does not equal 4, so this is a false statement.
This means the problems has no solution.
No matter what number you put in for x, the original equation can never be true.
So the answer is "No solution"

I hope that helps make it click for you.
• At , When Sal said that you could subtract 5x from both sides, and you subtract 5x from 2x, wouldn't the number result as a negative? •   At that point in the video, his equation is 2x + 3 = 5x - 2. He actually subtracts 2x, but when you subtract 5x from both sides, you have:

2x - 5x + 3 = 5x - 5x - 2

On the left side, you have 2x - 5x, which is -3x, and then you have that + 3, so you have -3x + 3 for the left hand side. For the right hand side, you have 5x - 5x - 2. The 5x - 5x part cancels out, leaving just a -2 for the right hand side.

-3x + 3 = -2

The next thing we can do is subtract 3 from both sides. We have the "+ 3" on the left side that can be eliminated there. Then the -2 on the right side becomes a -5. Subtracting a positive number from a negative numbers makes that number more negative.

-3x = -5

Now, I don't like having negative numbers in my equations, and since both sides are negative, I'll multiply both sides by -1 to convert these to positive numbers. That's the whole point in multiplying by -1, that we'll get positive numbers instead of negative numbers, and the equation is still valid because we'll be doing it to both sides. We get

3x = 5

Now, we can just divide both sides by 3. We get

X = 5/3

Thus, we've arrived at the same answer. I got slightly screwed up as I was trying to type this up, and that was because I had forgotten about the + 3 on the left side pretty early. I think it helps not to forget about that as you are trying to group the terms together. It's pretty easy to make that mistake when you group terms like that. That's what happened to me.

I hope this helps!
• I don't understand why he put 2 thirds if there was only one third at . • I'm a little confused on how you go back and check if you got the correct answer since you're left off with x=1 2/3. How would you go through and check your solution? • i can solve this, and i appreciate the demo. but my assignments don't give me problems like this, despite the fact that both of these are "solving equations with variables on both sides". why is that? • What practice set goes with this video? It would be great if there was a link to it, like there is from the practice sets to the appropriate video. (sorry if anyone already suggested this or if there is an easy way to find out that I just didn't see) -Protomas • Hi I am in 8th grade and in April I have the New York state exam it contains word problems with fractions and everything. Word problems are my biggest weakness where do I start • hi i have a question my math teacher said that you can also turn fractions into decimals is that true? and will that be on future tests? if so should i choose the fraction answer or decimal answer? • I still don't understand how to solve the unknown , why 2x + 3 = 5x - 2, can anyone explain it in detail? Thank you. • Let's go through it step-by-step:

1.) Write down the equation: 2x + 3 = 5x - 2

2.) Isolate the variable "x" on the right hand side:
[2x ( - 2x )] + 3 = [5x ( - 2x )]

3.) We get: 3 = 3x - 2, now er can add 2 to both sides:
[3 ( + 2 )] = 3x [- 2 ( + 2 )]

4.) We now get: 5 = 3x, now divide both sides by 3:
[5 ( / 3 )] = [3x ( / 3 )]

5.) We have our answer: x = 5/3, or x ≈ 1.7.

Hope this helped! 