Inequalities in One Variable

10-1Order of Real Numbers

Overview

a < b if a is to the left of b on the number line. ‘<,’ ‘>,’ ‘≤,’ ‘≥’ compare numbers.

Key ideas

  • a < b means b − a > 0.
  • Negatives reverse order.
  • Trichotomy: exactly one of a < b, a = b, a > b is true.

Worked examples

Example 1

Problem. Compare −5 and −2.

Solution. −5 < −2

Example 2

Problem. True or false: 3 ≥ 3?

Solution. True.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Compare 0 and −0.5.

  2. 2.

    True or false: −7 < −10?

  3. 3.

    Order from least to greatest: −1, 1/2, −3, 0.

Challenge problems

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

  1. 1.

    Compare: Is −3/4 > −5/6?

  2. 2.

    Arrange from least to greatest: 0.6, 2/3, 5/8, 0.55.