What this covers
Linear inequalities is taught in Year 12 (age 16 to 17, KS5) as a topic to introduce. It sits in the Algebra strand.
Worked example
Solve: 5 - 2x <= 13
- Subtract 5 from both sides: -2x <= 8
- Divide both sides by -2 and reverse the inequality sign: x >= 8 ÷ -2
- Simplify the result: x >= -4
Answer: x >= -4
Difficulty scale
The sheet generator offers five difficulty settings for this topic.
- One-step inequalities with positive integers, e.g., x + 3 > 7
- Two-step inequalities with positive coefficients, e.g., 2x - 5 <= 9
- Two-step inequalities requiring division by a negative, flipping the sign
- Inequalities with the variable on both sides, e.g., 4x + 1 > x + 10
- Double-ended inequalities, e.g., -3 <= 2x + 1 < 9, finding integer solutions
Common mistakes
- Forgetting to reverse the inequality sign when multiplying or dividing by a negative number
- Confusing strict inequalities (<, >) with inclusive ones (<=, >=) when plotting on a number line
Curriculum links
Indicative matches to National Curriculum for England. Check wording and codes against the official document.
- Solve quadratic equations and inequalities using factorisation, completing the square, and discriminant analysis.