Chapter 9: Review

The chapter problem, solved

Let $h$ be the number of hours. The first hall costs $18+6h$ pounds; the second costs $10+8h$ pounds.

Set the costs equal: $18+6h=10+8h$.

Subtract $10$ and $6h$: $8=2h$.

Divide by $2$: $h=4$.

At four hours, both halls cost £42. The equal point is after two hours, as you predicted or revised in the opener.

Mixed practice: choose a method and explain why

For each item, name the method before you work. After calculating, say why that method fits.

1. Solve $5x-7=18$.
2. Solve $4x+3=2x+15$.
3. A rectangle has length $x+5$ and width $x$. Its perimeter is 46 cm. Find its sides.
4. Write and solve an inequality for values no greater than 6.
5. Solve $3-2x<11$.

1. Solve $(x+1)(x-4)\geq0$.
2. Solve $x^2-2x-8<0$.

1. Chapter 1 link: estimate $19.8\times4.9$ and explain how the estimate checks an exact answer.

What you can now do

• solve linear equations and check them by substitution;
• form an equation from a context and interpret its solution;
• describe inequality solution sets with symbols and number lines;
• solve linear inequalities and reverse the sign when dividing by a negative;
• (Higher only) solve quadratic inequalities using roots and interval tests.

Your relevance reflection

Return to your example of comparing costs. Write the equation that models it, then explain what its solution means. What other situation could use the same method?