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All courses Math Foundations · MF.EQ.3 30 of 60
Combine like terms and simplify expressions while preserving structure.

Combine like variable terms

Problem
Simplify the expression 3x + 5x.
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Hint

Look at the two terms and notice they both have the same variable part: x.

These are like terms, so you add the coefficients and keep the x attached.

Solution walkthrough

01

Notice the like terms

\[3x~+~5x\]

Both terms have the same variable part, x. That means they are like terms and can be combined.

02

Combine the coefficients

\[3~+~5~=~8\]

When like terms have the same variable part, you add only the coefficients in front.

03

Keep the variable attached

\[3x~+~5x~=~8x\]

The x stays because both original terms were x-terms. Only the front numbers changed from 3 and 5 to 8.

04

State the simplified expression

\[8x\]

So the expression 3x + 5x simplifies to 8x.

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Another way

  1. Factor out x: 3x + 5x = (3 + 5)x = 8x.

!

Common mistake

Writing 8 instead of 8x. The coefficients combine, but the variable x must stay because both terms represent groups of x.