Chapter 9: Equations and inequalities
The chapter problem
A community hall hires a room for a fixed fee of £18, then charges £6 per hour. Another hall charges £10 plus £8 per hour. How many hours make the prices equal?
Before calculating, predict whether the equal point is before or after two hours. You can revise your prediction later.
By the end of this chapter you will be able to
- solve linear equations, including equations with an unknown on both sides;
- turn information from a situation into an equation and solve it;
- write inequalities, show their solutions on a number line, and use set notation;
- solve linear inequalities, including those divided by a negative number;
- solve quadratic inequalities by finding roots and checking intervals. (Higher only)
Roadmap
- 9.1 Solving linear equations
- 9.2 Equations with unknowns on both sides
- 9.3 Forming and solving equations
- 9.4 Inequalities on a number line and set notation
- 9.5 Solving linear inequalities
- 9.6 Quadratic inequalities (Higher only)
Your connection
A fixed fee plus a cost for each unit appears in many situations. Where might you or someone you know compare two such costs? Write your own example and say what the unknown would represent.