Inequalities summary

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

Dividing by a negative reverses the inequality.

Worked example 2 — Number line

Describe $x\ge2$ on a number line.

Working

Filled circle means included.

Worked example 3 — Both sides

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

Working

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.