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Absolute value equations worksheets

An absolute value equation has two answers, and seeing why is the whole lesson: |ax + b| = c says the inside is c away from zero, so it is c or it is −c. These free printable worksheets ask a child to split the bars into two ordinary equations and solve each.

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Ready to printAbsolute value equations
Absolute value equations worksheet — Split the bars, whole answers, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

The bars are the only new idea, and they mean distance. |x − 3| = 7 asks which numbers sit 7 away from 3 — one above, one below — so it splits into x − 3 = 7 and x − 3 = −7, giving 10 and −4. A child who forgets the second equation finds only the positive answer and misses half of every question, which is why every step-by-step walk here writes the split out before it solves.

Why this sheet works

Two levels build on the split. The first keeps the coefficient at one, so each equation is a single add or subtract away from the answer. The second puts a number in front — |3x − 18| = 3 — so after the split there is still a divide to do, and both answers come out whole because the numbers are chosen for it.

How this one works

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

Solve |2x − 6| = 8

2x − 6 = 8or2x − 6 = −8
2x − 6 = 8→x = 7
2x − 6 = −8→x = −1
x = −1orx = 7
  1. The bars mean the inside is 8 away from zero — so it is 8 OR it is −8. Split into two equations.
  2. Solve the first, 2x − 6 = 8: add 6 to both sides: 2x = 14, then divide by 2: x = 7.
  3. Solve the second, 2x − 6 = −8: add 6 to both sides: 2x = −2, then divide by 2: x = −1.
  4. So x = −1 or x = 7 — both answers.

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