9.3 Forming and solving equations — Practise with help
Warm-up: remember
Answer these from memory. Do not look back at the section.
- Write an expression for 5 more than .
- Solve .
Check the warm-up
- .
- .
If an answer differs, revisit Section 8.1 for writing expressions and Section 9.1 for solving equations.
Practise with help
1. Solve .
Hint
Undo addition, then multiplication.
Next step
Try the first operation or write the equation before opening the full solution.
Full working
Subtract : . Divide by : .
2. A number plus 9 is 23. Find it.
Hint
Let the number be and write an equation.
Next step
Try the first operation or write the equation before opening the full solution.
Full working
Let it be : , so .
3. Two consecutive integers total 25. Find them.
Hint
Let the smaller integer be ; the next is .
Next step
Try the first operation or write the equation before opening the full solution.
Full working
Equation , so . The integers are and .
4. A rectangle has width and length . Its perimeter is 28 cm. Find its sides.
Hint
Use perimeter = two widths + two lengths.
Next step
Try the first operation or write the equation before opening the full solution.
Full working
, so and . Length cm.
5. A club charges £4 to join and £3 per visit. The total is £25. Find the visits.
Hint
Let be the visit count.
Next step
Try the first operation or write the equation before opening the full solution.
Full working
Equation , so and .