Algebra (all units) · Both
Inequalities
Solving linear inequalities, representing solutions on a number line, and double inequalities.
Inequalities use < > ≤ ≥. Solve them like equations, but reverse the inequality sign when multiplying or dividing by a negative number.
Solving linear inequalities
Treat like an equation:
• Add/subtract the same value on both sides
• Multiply/divide both sides by a positive number (sign stays the same)
• Multiply/divide by a negative → reverse the inequality sign
Worked example
Solve: 3x − 5 > 10
Solution
3x − 5 > 10 Add 5: 3x > 15 Divide by 3: **x > 5**
Reversing the sign
When you multiply or divide by a negative number, reverse the inequality.
Worked example
Solve: −2x ≤ 8
Solution
Divide by −2 and reverse: **x ≥ −4**
Number line representation
• Open circle ○ for < or >
• Closed circle ● for ≤ or ≥
• Arrow shows the direction of the solution set
Practice questions
Try these without looking at the answers first.
Q1.Solve: 2x + 3 < 11
Show answer
x < 4
Q2.Solve: −3x ≥ 12
Show answer
x ≤ −4
Q3.Solve: 5 − 2x > 1
Show answer
x < 2