Grade 11 · Mathematics
Absolute value
Why it matters
Definition and graphs.
Last reviewed 2026-09-03 · accuracy standard
What is absolute value?
Short answer
The absolute value of a number is its distance from zero on the number line, so it is never negative. It is written with vertical bars: |5| = 5 and |−5| = 5. Formally, |x| = x when x ≥ 0 and |x| = −x when x < 0. Because it measures distance, absolute value appears whenever only magnitude matters.
Concept preview
What you will be able to do
- 01Interpret absolute value as distance from zero and evaluate expressions
- 02Graph and read the vertex of a translated absolute-value graph
- 03Solve absolute-value equations (and simple inequalities), checking for no-solution cases
You already have the right instinct for this: if a friend is 5 steps to your left or 5 steps to your right, they are 5 steps away either way — direction does not change the distance. Absolute value captures exactly that. The absolute value of a number, written , is its distance from zero on the number line, and distance is never negative. So and : both are 5 units from zero. The bars simply say 'forget the sign, tell me how far'.
School Plan
Absolute value
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Related topics
Frequently asked questions
- Can absolute value be negative?
- No. It represents distance from zero, which is always zero or positive.
- How do you solve an absolute value equation like |x| = 3?
- Consider both cases: x = 3 and x = −3, since both are distance 3 from zero.