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.

### Course: Algebra 1>Unit 2

Lesson 1: Linear equations with variables on both sides

# Intro to equations with variables on both sides

Learn how to solve the equation 2x + 3 = 5x - 2 with the variable on both sides. We start by visualizing the equation, then isolate the variable by performing the same operations on both sides. Finally, we solve the equation to find the value of the variable. 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.
• 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?
• plugin 5/3 for x then solve and see if the statement is true for example if you get 4=9 then 5/3 is wrong but if you get something like 4=4 or 0=0 then you are correct.
• Can someone explain this a lot easier I'm just sitting and my brain is fried?
• Your goal is to create: x = a number.

1) When you have the variable on both sides, start by moving all the Xs to one side of the equation. In the example from the video, this means you need to move either the 2x or the 5x to the other side. It doesn't matter which you pick to move. Just pick one and use the opposite operation to move it. Sal chose to move 2x. Since 2x is positive, he must subtract 2x from both sides.

2) Once you have only one term containing x, any number on the same side as X must be moved to the other side, again by using opposite operations.
-- Start by moving the constant term (the one without the variable. This is where Sal adds 2 to both sides of the equation.
-- Then, if there is any coefficient other than 1 in front of the variable, then you would use division to move the coefficient to the other side. This is where Sal divides the equation by 3.

Hope this helps.
• 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
• Equations with variables on both sides. If you are watching this in the 8th grade (US)- Solving equations section it should be under this video on the list of videos and practice tasks.
• For anyone who is confused, this is how to solve 2x+3 = 5x-2 easier

2x+3 = 5x-2
First off we need to isolate the similar terms on both sides.
We can do this just by transposing it to the other side, but remember to change the sign whenever your transposing a number to the other side.
We can change it in this format:
(Terms with variables) = (Numbers only)
so 2x - 5x (the positive 5x changed into a negative 5x since we are transposing it)
2x - 5x = -2 -3 (same here)
so 2x - 5x = -3x
-2 - 3 = -5
so we get -3x = -5
divide by -3 to both sides to cancel out the negative 3
x= -5/-3 which is also equal to 5/3 :))
hope this helpss!
• 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
• The way I do it on exams is change the word problem into an equation, solve the equation and add the appropriate ending.
• 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!
• 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?
• The decimal for is neater but Khan tends to ask for the fraction form of an answer. To turn a decimal into a fraction put it over 10 100 1000 depending on how many places it's asking for then simplify.
• So, I was doing the practice... How do I know which number I have to add to the variables?