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➖ Inequalities on a Number Line

Turn statements like 'at least 12' into x ≥ 12, solve simple inequalities with the same moves you use for equations, and draw the answers on a number line.

lesson

~15 min

to learn

🔢 Math

subject

Ages 6–12

level

Start the course →

What you’ll learn

Numbers on a number lineWrite inequalities from worded constraints, solve simple linear inequalities using inverse operations, and represent solutions on a number line with open or closed circles.An inequality compares amounts with <, >, ≤, or ≥, where the line under ≤ and ≥ adds 'or equal to'. Worded rules translate directly: 'at least 12' is x ≥ 12, 'under 50' is x < 50. Simple inequalities are solved with the same inverse-operation moves as equations — 2x + 1 ≤ 9 gives x ≤ 4 — with one extra rule: flip the sign if you multiply or divide by a negative. On a number line, a closed circle marks an included boundary (≤, ≥) and an open circle an excluded one (<, >), with shading over the whole solution range.

Questions this course answers

What does the symbol ≥ mean?

The line under the > adds 'or equal to': greater than or equal to.

How do you write 'a number x is at least 12'?

'At least 12' means 12 or more, which is x ≥ 12.

On a number line, which inequality uses an OPEN circle?

A strict < (no 'or equal to') excludes the boundary, so it's an open circle.

Solve 2x + 1 ≤ 9.

Subtract 1 to get 2x ≤ 8, then divide by 2 to get x ≤ 4.

Which inequality would be drawn with a CLOSED circle?

≥ includes the boundary value, shown by a closed (filled) circle.

Solve 3x − 2 ≥ 7.

Add 2 to get 3x ≥ 9, then divide by 3 to get x ≥ 3.

Grounded in trusted sources

BBC Bitesize — Maths (Key Stage 3)
Khan Academy — Inequalities
NRICH (University of Cambridge)
Britannica

Every Wunder lesson is built from real, reputable sources — never invented.

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