Absolute Value Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Absolute Value.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The distance of a number from zero on the number line, always non-negative; written |x|.

-5 and 5 are both 5 units from zero, so |-5| = |5| = 5.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Absolute value strips away the sign, leaving only magnitude.

Common stuck point: Confusing |-x| with -|x|: |-3| = 3 but -|{-3}| = -3. Always non-negative inside.

Sense of Study hint: Draw a number line and count the steps from the number to zero -- that count is the absolute value.

Worked Examples

Example 1

easy
Evaluate |{-7}| + |3|.

Solution

  1. 1
    The absolute value of -7 is the distance from 0: |{-7}| = 7.
  2. 2
    The absolute value of 3 is |3| = 3.
  3. 3
    Add: 7 + 3 = 10.

Answer

10
Absolute value measures distance from zero on the number line and is always non-negative. For any number a, |a| = a if a \ge 0 and |a| = -a if a < 0.

Example 2

medium
Evaluate |5 - 12| - |2 - 9|.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Evaluate |{-15}| - |{-4}|.

Example 2

medium
Evaluate |3 - 8| + |{-2}| - |5|.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

integers