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Number Lines and Solution Sets (F)

Number Lines and Solution Sets (F)

Read inequalities on number lines. Use open and closed circles, shading, and set notation to show solution sets accurately in GCSE Maths Foundation.

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Fascinating Fact:

In temperature safety, −2 < x ≤ 5 means above −2 but up to 5, so open at −2, filled at 5, and shade between, because −2 fails the rule but 5 passes.

In GCSE Maths, number lines help you visualise inequality solutions. You’ll interpret symbols, choose open or closed circles, shade intervals, and switch between inequality, interval, and set notation with care.

Key Terms

Inequality: A statement comparing values using <, ≤, >, or ≥ instead of an equals sign.
Solution set: All numbers that make an inequality true, often shown on a number line or in set notation.
Open/closed circle: Open means the endpoint isn’t included; closed (filled) means the endpoint is included.

Frequently Asked Questions (Click to see answers)

How do I show inequalities on a number line?

Plot endpoints, use an open circle for < or >, a closed circle for ≤ or ≥, then shade all values that satisfy the inequality.

What does an open and a closed circle mean in GCSE inequalities?

An open circle means the endpoint is not included. A closed (filled) circle means the endpoint is included in the solution set.

How do I write a solution set from a number line?

Read the shaded region and endpoints. Write using inequalities (e.g., −2 < x ≤ 5) or set notation { x : −2 < x ≤ 5 }.

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

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