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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
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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 terms on the left

\[3x~+~5~+~2x~=~25~\;\rightarrow\;~5x~+~5~=~25\]

The terms 3x and 2x are like terms because they both have x. Adding them gives 5x, while the +5 stays the same.

02

Subtract 5 from both sides

\[5x~+~5~=~25~\;\rightarrow\;~5x~=~20\]

Subtracting 5 undoes the +5, so the variable term is isolated more clearly. Doing the same thing to both sides keeps the equation balanced.

03

Divide by the coefficient of x

\[5x~=~20~\;\rightarrow\;~x~=~4\]

Since 5x means 5 times x, divide both sides by 5 to get x by itself.

04

State the solution

\[x~=~4\]

The value that makes 3x + 5 + 2x equal 25 is 4.

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Another way

  1. Check by substitution: if x = 4, then 3(4) + 5 + 2(4) = 12 + 5 + 8 = 25, so the solution works.

!

Common mistake

A common mistake is to combine 5 and 2x and write 7x. That is wrong because 5 is a constant and 2x is a variable term, so they are not like terms.