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
Before this, every equation a student solves has exactly one answer, so |x + 3| = 7 is often the first time two different answers are both correct — and that idea alone is worth the practice.
How to do it
- To evaluate, work out what's inside, then make the result positive.
- To solve |expr| = c, split into two cases: expr = c and expr = −c.
- Solve each case; you'll usually get two answers.
Examples by level
- Beginner|2| =Answer2
- Intermediate|x − 1| = 8Answerx = 9 or x = −7
- Advanced|x − 12| = 10Answerx = 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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