GOZUNTA
Try it now
All courses Math Foundations · MF.EQ.7 34 of 60
Solve multi-step linear equations, including equations requiring simplification first.

Simplify first, then solve

Problem
Combine like terms, then solve for \(x\): \(3x~+~5~+~2x~=~25\)
Your answer
Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
With a free account

Save the work you do.

Your session results stay with your account, so today’s practice can inform what you work on next.

Create a free account
With paid access

Revisit a weak spot without repeating one problem.

Use additional variants to practice the same idea again while still having to do the mathematics.

Compare plans

Hint

Start by combining the like terms on the left: 3x and 2x. Then rewrite the equation in simpler form.

Like terms have the same variable part. 3x and 2x combine, but the constant 5 stays separate.

Solution walkthrough

01

Combine the like variable terms

\[3x~+~2x~=~(3~+~2)x~=~5x\]

Both variable terms have the same x factor, so their coefficients add.

02

Rewrite the equation

\[5x~+~5~=~25\]

Combining like terms leaves one variable term and the constant 5.

03

Undo addition and multiplication

\[5x~=~25~-~5~=~20;~x~=~20/5~=~4\]

Subtract 5 from both sides, then divide both sides by 5.

04

Check and report

\[x~=~4\]

Three times four plus five plus two times four is twelve plus five plus eight, or twenty-five.

+

Another way

  1. Substitute candidate values only as a check; the direct solve combines to 5x, removes 5, and divides by 5.

!

Common mistake

Do not begin isolating x while leaving 3x and 2x separate. Combining them first reduces the equation to 5x + 5 = 25.

Solution walkthrough video