Examples and practice
Solving inequalities
Back to lessonPractice section 1 · Questions 1–6
Read the same interval from a parabola and a sign line · Check a repeated root and include isolated equality solutions · +4 more
- Read the same interval from a parabola and a sign line
- Check a repeated root and include isolated equality solutions
- Use a difference graph, two graphs or a factored sign line
- Discard an always-positive factor safely
- Keep a denominator zero separate from allowed endpoints
- Keep the sign of x when solving a rational inequality
Practice section 2 · Questions 7–12
Prove a quadratic is positive before removing it · Use either a difference graph or a denominator sign test · +4 more
- Prove a quadratic is positive before removing it
- Use either a difference graph or a denominator sign test
- Check the radical domain before reading or squaring the inequality
- Keep both radical endpoints strict in self-practice
- Choose inside or outside intervals for a modulus comparison
- Keep the parameter when translating a modulus interval
Practice section 3 · Questions 13–18
Compare two moduli using a difference or two graphs · Recognise the same rational inequality after a substitution · +4 more
Practice section 4 · Questions 19–24
Rational inequalities with transformed inputs · Find a range using the discriminant · +4 more
Practice section 5 · Questions 25–30
A rational identity and a scaled input · Transfer a rational inequality to logarithmic inputs · +4 more
Practice section 6 · Questions 31–36
Use a nonpositive squared input · Compare squared and reflected inputs · +4 more
Practice section 7 · Questions 37–38
A parameter hyperbola and a logarithmic input · Use two distinct real roots to restrict a parameter