AlgebraStructure & Method · Book 1All Chapters

Numbers on a Line

1-9Opposites and Absolute Values

Overview

Opposite numbers are the same distance from 0 but on different sides. Absolute value is the distance from 0 and is always ≥ 0.

Key ideas

  • The opposite of a is −a.
  • |a| = a if a ≥ 0; |a| = −a if a < 0.
  • |0| = 0; the opposite of 0 is 0.

Worked examples

Example 1

Problem. Find |−7|.

Solution. 7

Example 2

Problem. Find the opposite of 4.

Solution. −4

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Evaluate |9|.

  2. 2.

    Evaluate |−12|.

  3. 3.

    What is the opposite of −5?

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Simplify |−8| + |3| − |−5|.

  2. 2.

    If |x| = 6 and |y| = 2, what is the greatest possible value of |x − y|?