Absolute Value · Grades 6–8

Absolute Value Worksheets

Distance from zero, which is why the answer is never negative. Worksheets from evaluating |−8| up to equations like |x + 3| = 7, where two answers are both right.

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What it is

The absolute value of a number is its distance from zero, so it is never negative. |−5| and |5| both equal 5.

Why it matters

Absolute value formalizes distance and magnitude, and it's the first place students meet equations with two solutions, key groundwork for later algebra.

How to do it

  1. To evaluate, work out what's inside, then make the result positive.
  2. To solve |expr| = c, split into two cases: expr = c and expr = −c.
  3. Solve each case; you'll usually get two answers.

Examples by level

  • Beginner|2| =2
  • Intermediate|x − 1| = 8x = 9 or x = −7
  • Advanced|x − 12| = 10x = 22 or x = 2

Examples are generated by the same engine as the worksheets, so they're always mathematically correct. Built to avoid repeats, not reshuffle the same handful of questions.

Common mistakes

  • Thinking |−5| is −5 instead of 5.
  • Giving only one solution to |x| = a (there are two: a and −a).
  • Dropping the second case when solving |x + b| = c.

Tips

  • Absolute value is never negative.
  • An equation |expr| = c (with c > 0) has two solutions.

For parents

Absolute value asks 'how far from zero?', distance is always positive, so the answer is never negative.

For teachers

Emphasize the two-case setup for equations: |expr| = c means expr = c OR expr = −c.

Key vocabulary

absolute value
a number's distance from zero, always ≥ 0

Frequently asked questions

What does absolute value mean?
It's the distance of a number from zero on the number line, so it's always zero or positive.
Why does |x| = 5 have two answers?
Both 5 and −5 are a distance of 5 from zero, so x can be either.

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