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Combining like terms worksheets

Collecting like terms is tidying up: the x parts go together, the plain numbers go together, and nothing else moves. These free printable worksheets ask for the simplified expression, written as a coefficient and a constant.

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Ready to printCombining like terms
Combining like terms worksheet — One variable, two blanks, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

The idea is easier than the notation makes it look. 4x + 3 + 2x + 5 is four x's and two more x's, which is six x's, plus eight. Saying it in words first — "six x's and eight" — is usually enough to unstick a child who is staring at the symbols, because they have been adding six of something to two of something since they were five.

Why this sheet works

What cannot be combined is the part worth insisting on. 6x + 8 does not become 14x, however much a child would like a single answer, because x is not 1. Asking "six whats and eight whats?" makes the mismatch audible.

How this one works

One question from this sheet, worked through a step at a time.

7x + 5x + 15

7x + 5x + 15
7 + 5=12
15=15
12x+15
  1. There are two kinds of thing on this line and they cannot mix: the x terms, and the plain numbers. Sort them into two piles before adding anything — the x terms are 7x and 5x, and the numbers are 15.
  2. Add up the x pile, keeping the signs: 7 + 5 = 12, so 12x.
  3. There is only one plain number, so that pile is already done: 15.
  4. So it is 12x + 15 — and that is finished, even though it is still two things. Squashing them into 27x would be answering "12 whats and 15 whats?", and there is no answer to that until somebody says what x is.

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