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Linear Inequalities (F)

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Linear Inequalities (F)

Solve GCSE Foundation inequalities. Use number lines, inverse operations, and careful sign flips when multiplying or dividing by negatives to describe solution sets.

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Fascinating Fact:

For DIY planks, length 9 − 3x must be ≥ 0 to fit, so −3x ≥ −9 gives x ≤ 3 after dividing by −3 and flipping the sign.

In GCSE Maths (Foundation), linear inequalities compare values using symbols like <, ≤, >, and ≥. You’ll solve step by step, flip the sign when multiplying or dividing by a negative, and show solutions on number lines.

Key Terms

Inequality: A statement comparing quantities with <, ≤, >, or ≥ instead of equals.
Solution set: All numbers that make the inequality true (often shown on a number line).
Number line: A diagram marking values; open circle for </>, closed circle for ≤/≥ with shading for the range.

Frequently Asked Questions (Click to see answers)

How do you solve a linear inequality step by step?

Use inverse operations as with equations: add/subtract, then multiply/divide. If you multiply or divide by a negative, flip the inequality sign.

When do I reverse the inequality sign?

Reverse the sign only when you multiply or divide both sides by a negative number. For example, −2x > 8 becomes x < −4.

How do I show solutions on a number line?

Use an open circle for < or > and a closed circle for ≤ or ≥, then shade in the direction of the values that satisfy the inequality.

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You can find more about this topic by visiting BBC Bitesize - Inequalities

Author: Sally Thompson (MSc Operational Research, Secondary Maths Teacher & Quiz Writer)

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