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.
Compare 0 and −0.5.
- 2.
True or false: −7 < −10?
- 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.
Compare: Is −3/4 > −5/6?
- 2.
Arrange from least to greatest: 0.6, 2/3, 5/8, 0.55.