How to Solve a Simple Linear Equation

You need to find out what $x$ equals if you have a problem like $7x-10=3x+6$ . This kind of equation is called a linear equation,^{[1]XResearch source} and it usually has just one variable. This article will walk you through the simple steps.

Method 1

Method 1 of 2:

Starting with the Variables on Opposite Sides

Download Article

A simple linear equation might look like $7x-10=3x-6$ .^{[2]XResearch source}
2
Check the equation for varying terms and constant terms. Varying terms are numbers like $7x$ $How.com.vn English: 7x$ , $3x$ $How.com.vn English: 3x$ , $6y$ $How.com.vn English: 6y$ or $10z$ $How.com.vn English: 10z$ , where the number changes depending on what you plug into the variable, or letter. Constant terms are numbers like $10$ $How.com.vn English: 10$ , $6$ $How.com.vn English: 6$ or $30$ $How.com.vn English: 30$ , where the number never changes.
- Usually, equations won't come with varying terms and constant terms lined up on separate sides. In the example above, the left-hand side (LHS) has both varying and constant terms, as does the right-hand side (RHS).
Advertisement
3
Prepare to move the numbers around so that the varying terms are on one side and the constant terms are on the side^{[3]XResearch source} such as in $16x-5x=32-10$ (that equation is solved in example 2). In order to do this, you may have to subtract or add the numbers you want to move from both sides. In the next step, you'll see how to do that in example 1.
- The equation $16x-5x=32-10$ does have all the varying terms on one side (LHS), while all the constant terms are on the other side (RHS).
4
Move the varying terms to one side of the equation. It doesn't matter to which side you move the varying terms.
- In example 1, $7x-10=3x-6$ can be rearranged by choosing to subtract either $7x$ or $3x$ from both sides. Choosing to subtract $7x$ , you have:
  
  ${\begin{aligned}(7x-7x)-10&=(3x-7x)-6\\-10&=-4x-6\end{aligned}}$
5
Bring all the constant terms onto the other side of the equation. That is: move the constant terms so that they are on the opposite side of the equation from where the varying terms are.^{[4]XResearch source}
- We see that $-6$ must be subtracted from both sides:
  ${\begin{aligned}-10-(-6)&=-4x-6-(-6)\\-4&=-4x\end{aligned}}$
$How.com.vn English: Step 6 Divide both sides by the coefficient of x {\displaystyle x} .$
6
Divide both sides by the coefficient of $x$ . The coefficient of $x$ $How.com.vn English: x$ (or $y$ $How.com.vn English: y$ , or $z$ $How.com.vn English: z$ , or any letter) is the number in front of the varying term.^{[5]XResearch source}
- The coefficient of $x$ in $-4x$ is $-4$ . So divide both sides by $-4$ to get the value of $x=1$ .
- Our answer to the equation $7x-10=3x-6$ is $x=1$ . You can check this answer by plugging $1$ back into every $x$ variable and seeing if both sides of the equation equal the same number:
  ${\begin{aligned}7(1)-10&=3(1)-6\\-3&=-3\end{aligned}}$

Method 2

Method 2 of 2:

Starting with the Variables on One Side

Download Article

1
Know that sometimes the varying terms and the constant terms will be separate. Sometimes, half of your work will be done for you. You'll have all the varying terms on one side and all the constant terms on the other side. If this is the case, all you have to do is the following.
For the equation $16x-5x=32-10$ , we just have to subtract the numbers from one another.^{[6]XResearch source}
$How.com.vn English: Step 3 Next, divide both sides by the coefficient of x {\displaystyle x} .$
3
Next, divide both sides by the coefficient of $x$ . Remember that the coefficient of x is the number in front of the varying term.^{[7]XResearch source}
- In this example, the coefficient of $x$ in $11x$ is $11$ . That division is $11x/11=22/11$ to get $x=2$ . The answer to the equation $16x-5x=32-10$ is $x=2$ .

Community Q&A

Search

Add New Question

Question
How do I answer (1 - 0.9)(1 - 0.2)?
Donagan
Top Answerer
That's (0.1)(0.8) = 0.08.
Thanks! We're glad this was helpful.
Thank you for your feedback.
If How.com.vn has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission.Support How.com.vn
Yes No
Not Helpful 15 Helpful 8
Question
How do you solve a question like, x-5=7?
Community Answer
In this example, move the 5 to the other side and change your action symbol, like this: x=7+5. Now, you can solve for x. To be sure you've done it correctly, put in your value for x in the original equation and solve.
Thanks! We're glad this was helpful.
Thank you for your feedback.
If How.com.vn has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission.Support How.com.vn
Yes No
Not Helpful 10 Helpful 23
Question
How do I solve it if there are two variables?
Donagan
Top Answerer
You need two separate equations in those two variables.
Thanks! We're glad this was helpful.
Thank you for your feedback.
If How.com.vn has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission.Support How.com.vn
Yes No
Not Helpful 15 Helpful 10

See more answers

Ask a Question

200 characters left

Include your email address to get a message when this question is answered.

Submit

Tips

Submit a Tip

All tip submissions are carefully reviewed before being published

Submit

Thanks for submitting a tip for review!

Warnings

Why do it that way? Trying to divide this: $4x-10=-6$ like this $4x/4-10/4=-6/4$ creates $x-10/4=-6/4$ with a lot of fractions to handle, and that's not so easily solved; so, simplifying is one good reason to get all the variable terms onto one side and all the constant terms onto the other side.
Thanks
Helpful0 Not Helpful0