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Algebra · Foundation & Higher

Inequalities

Inequalities show that one expression is greater than, less than, or equal to another. They are solved like equations, with one important exception.

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Key facts to remember

  • 1< means "less than", > means "greater than", ≤ means "less than or equal to", ≥ means "greater than or equal to".
  • 2Solve inequalities like equations — but if you multiply or divide by a negative number, flip the inequality sign.
  • 3The solution to a linear inequality is a range of values.
  • 4On a number line: open circle ○ for strict inequalities (< or >); closed circle ● for ≤ or ≥.
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Worked examples

Example 1

Solve 3x − 4 > 11 and represent on a number line.

Working

  1. Add 4 to both sides: 3x > 15
  2. Divide by 3: x > 5
  3. Number line: open circle at 5, arrow pointing right
Answerx > 5
Example 2

List the integers that satisfy −2 ≤ x < 4

Working

  1. x can be −2, −1, 0, 1, 2, 3 (not 4, since x < 4)
Answer−2, −1, 0, 1, 2, 3
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Common mistakes

✗Not flipping the sign when multiplying or dividing by a negative number.
✗Including the endpoint for a strict inequality (< or >) when listing integers.
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Exam tips

✓If a question says "integer values", list them — don't just write the inequality.
✓Check by substituting a value from your solution range back in.

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