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Variables on both sides worksheets

5x + 3 = 2x + 18 is the first equation that needs a decision before it needs arithmetic. These free printable worksheets practice collecting the x terms and then solving.

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Ready to printVariables on both sides
Variables on both sides worksheet — Whole-number solutions, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Every equation before this one has x in a single place, so the only question is what to undo. Here a child who starts by subtracting the 3 has not done anything wrong — they have just done it in an order that leaves them no better off, because there is still an x on the other side. Collecting the x terms first is the new move, and once it is done the equation is a two-step one they have already met.

Why this sheet works

Both orientations are on every sheet on purpose. 5x + 3 = 2x + 18 collects on the left and 2x + 18 = 5x + 3 collects on the right, and a page of only the first teaches "always move the right one over" — a rule that breaks on the first mirrored equation a textbook prints. Deciding which side to collect on is the skill.

How this one works

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

4x + 15 = 2x + 23

4x + 15=2x + 23
4x + 15 = 2x + 23
2x + 15 = 23
2x + 15=23
2x + 15=23
2x=8
2x=8
x=4
4x + 15 = 2x + 23
31 = 31✓
  1. This one has x on BOTH sides, so nothing can be undone yet — subtracting 15 would still leave an x on the right. Collect the x terms first.
  2. Take 2x off BOTH sides. That clears x from the right, leaving 2x + 15 = 23. That is an equation you have already met.
  3. Two things were done to x: multiplied by 2, then 15 added. Undo them in the REVERSE order — whatever happened last comes off first.
  4. The 15 went on last, so it comes off first — and off BOTH sides, or the two halves stop being equal. 23 − 15 = 8.
  5. That leaves 2x, which means 2 lots of x. Divide both sides by 2: 8 ÷ 2 = 4.
  6. Check by putting it back into the ORIGINAL, both sides: 4(4) + 15 = 31, and 2(4) + 23 = 31 — both 31, so x = 4.

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