Topic summary · Foundation · CIE Core

Inequalities summary

Inequalities use $<,>,\le,\ge$ . Solving mirrors equations, except multiplying/dividing by a negative reverses the sign.

Open Learning Sheet — Inequalities Download Inequalities answers PDF

Files: foundation-28 Inequalities handout.pdf · foundation-28 Inequalities handout answers.pdf · free public downloads · diagrams in the PDFs

Key learning points

Represent on a number line: open circle for $<$ / $\gt$ , filled for $\le$ / $\ge$ .
Reverse the inequality when multiplying or dividing by a negative.
Integer solutions: list values that satisfy the inequality.

Worked example 1 — Solve and reverse

Solve $-2x>6$ .

Working

x<-3

Dividing by a negative reverses the inequality.

Worked example 2 — Number line

Describe $x\ge2$ on a number line.

Working

\text{closed circle at 2, arrow right}

Filled circle means included.

Worked example 3 — Both sides

Solve $3x-1\le 2x+5$ .

Working

x\le6

Collect like terms.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.

Open Learning Sheet Answers PDF

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