An inequality is like an equation but instead of an equals sign you have <, >, ≤, or ≥. The rules for solving them are almost identical to equations, with one critical exception: when you multiply or divide by a negative number, you flip the inequality sign.
Solving linear inequalities
Example: Solve 3x - 7 > 2 Step 1: Add 7 to both sides → 3x > 9 Step 2: Divide by 3 → x > 3 The solution is all real numbers greater than 3. On a number line, draw an open circle at 3 and an arrow pointing right.
The sign-flip rule
Example: Solve -2x ≥ 8 Divide both sides by -2 AND flip the sign: x ≤ -4 Why? Because multiplying or dividing an inequality by a negative number reverses the order of the number line. This is the rule students most often forget in the exam.
Double inequalities
Example: Find the integer values of x such that -3 ≤ 2x + 1 < 7 Subtract 1 from all three parts: -4 ≤ 2x < 6 Divide by 2: -2 ≤ x < 3 Integer values: x = -2, -1, 0, 1, 2
Key points
- Treat inequalities like equations: except the flip rule
- Multiply/divide by a negative: flip the sign
- Open circle on number line = strict inequality (< or >)
- Closed circle = includes that value (≤ or ≥)
- Always state the integer values if the question asks
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WAEC tip
WAEC sometimes combines inequalities with word problems ('a student needs at least...'). Read the question carefully to know whether the boundary value is included.
Practise this
Solve -5 < 3x - 2 ≤ 10. Show the solution on a number line and list all integer values of x.
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