Solving Inequalities
This topic covers 4 learning steps, guiding your child from the basics through to confident problem-solving. Each step includes a worked example and adaptive practice questions.
What Your Child Will Learn
- Read inequality symbols
Understand <, >, ≤, ≥ - Solve one-step inequalities
Solve x + 3 > 7 - Solve two-step inequalities
Solve 2x - 1 < 9 - Negative coefficient reversal
Reverse the sign when multiplying by negative
Common Mistakes
- Treating the inequality sign like an equals sign and forgetting to flip it when multiplying or dividing by a negative number
When you multiply or divide both sides of an inequality by a NEGATIVE number, the sign FLIPS. For example, -2x > 6 becomes x < -3 (not x > -3). This is the single most important rule in inequalities. - Not understanding the difference between < and ≤ (or > and ≥), especially when representing on a number line
< and > use an OPEN circle on the number line (the value is NOT included). ≤ and ≥ use a FILLED circle (the value IS included). Think of ≤ as "less than or equal to" — the line under the < means "or equal."
Tips for Parents
- Solve inequalities the same way as equations, but watch out for the sign-flip rule with negatives. Practise: "Solve -3x < 12" — divide by -3 AND flip, giving x > -4.
- Draw number lines: an open circle means "up to but not including" and a filled circle means "up to and including." Shade the direction of the solution.
- Use real-life examples: "You need at least £50 to buy the game. You have £15 and earn £5 per chore. How many chores do you need?" 15 + 5x ≥ 50, so x ≥ 7.
- Compare with equations: "Solving 2x + 3 = 11 gives x = 4. Solving 2x + 3 < 11 gives x < 4 — the method is identical except you keep the inequality sign."
Key Words
- Inequality — A mathematical statement using < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to) instead of =.
- Solution set — All the values that make the inequality true — for x > 3, the solution set is every number bigger than 3.
- Open circle — A hollow circle on a number line showing that the value is NOT included — used for < and >.
- Filled circle — A solid circle on a number line showing that the value IS included — used for ≤ and ≥.
- Integer solutions — The whole number values that satisfy the inequality — for 2 < x ≤ 5, the integer solutions are 3, 4, and 5.
Where This Fits
Before this topic: Children should be confident solving two-step linear equations and understand negative numbers on a number line.
After this topic: Inequalities lead to graphical inequalities (shading regions), quadratic inequalities, and linear programming at GCSE and A-level.
How MathCraft Teaches This
In MathCraft, Solving Inequalities is taught through the Algebra & Arithmetic adventure track. Your child follows guided lessons with friendly characters, works through examples step by step, then practises with questions that adapt to their level.
The adaptive engine tracks mastery across all 4 steps, revisiting concepts your child finds tricky and advancing when they're ready. Parents can see detailed progress in the Parent Dashboard.
Practise Solving Inequalities with MathCraft
Step-by-step lessons, worked examples, and adaptive practice — all wrapped in an adventure game your child will love.
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