Combining like terms

Why does

2 x + 3 x = 5 x

Please take time to think about this question on your own before looking at the answers below.

Practice problems

Use what you learned above to complete some practice problems.

Simplify.

5 x + 4 x

Simplify.

2 x + 4 x + x

Simplify.

8 x - 2 x

Simplify.

2 x + 5 y + 3 x

The problems you've just solved are examples of what we call combining like terms.

What are "like terms"?
In the expression

2 x + 5 y + 3 x

, there are three terms, but only two of them are "like terms". Like terms have the same variable part.

Like terms: $2 x$ ‍ and $3 x$ ‍

Unlike terms: $2 x$ ‍ and $5 y$ ‍

What does it mean to "combine" like terms?
Like terms can be "combined" by adding their coefficients (the numbers in front of the variables):

$2 x + 5 y + 3 x$ ‍
$= 2 x + 3 x + 5 y$ ‍
$= 5 x + 5 y$ ‍

Combine like terms.

z + x - y + 5 z + 3 y

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