Inequalities

An inequality says one side is bigger or smaller: < less than, > greater than, ≤ less than or equal to, ≥ greater than or equal to. Solve them like equations, but if you multiply or divide by a negative number, flip the sign.

Key facts

  • x > 3 means any number bigger than 3 (not 3 itself).
  • On a number line: an open circle for < and >, a filled circle for ≤ and ≥.
  • Multiplying or dividing by a negative flips the inequality.
  • Integers that satisfy −2 < n ≤ 1 are −1, 0 and 1.

Worked examples

Example 1

Solve 3x − 4 < 11.

  1. Add 4 to both sides. 3x < 15
  2. Divide by 3. x < 5

Answer: x < 5

Example 2

List the integers that satisfy −3 ≤ n < 2.

  1. Start at −3 (it’s included because of ≤).
  2. Stop before 2 (it’s not included because of <). −3, −2, −1, 0, 1

Answer: −3, −2, −1, 0, 1