Inequalities summary

Key learning points

• Critical values: zeros of numerator and denominator.
• Use a sign table or sketch to read where the inequality holds.
• Avoid multiplying by expressions that might be negative — use squared positives instead.
• Give answers as intervals or combined inequalities.

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.

Worked example 4 — Critical values

For $\frac{x-1}{x+2}>0$, which critical values appear?

Working

Roots of numerator and denominator.

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.