GCSE Mathematics (9-1)

9.3 Forming and solving equations — Practise with help

Warm-up: remember

Answer these from memory. Do not look back at the section.

  1. Write an expression for 5 more than nn.
  2. Solve 2x+3=112x+3=11.
Check the warm-up
  1. n+5n+5.
  2. x=4x=4.

If an answer differs, revisit Section 8.1 for writing expressions and Section 9.1 for solving equations.

Practise with help

1. Solve 3x+2=143x+2=14.

Hint

Undo addition, then multiplication.

Next step

Try the first operation or write the equation before opening the full solution.

Full working

Subtract 22: 3x=123x=12. Divide by 33: x=4x=4.

2. A number plus 9 is 23. Find it.

Hint

Let the number be nn and write an equation.

Next step

Try the first operation or write the equation before opening the full solution.

Full working

Let it be nn: n+9=23n+9=23, so n=14n=14.

3. Two consecutive integers total 25. Find them.

Hint

Let the smaller integer be nn; the next is n+1n+1.

Next step

Try the first operation or write the equation before opening the full solution.

Full working

Equation 2n+1=252n+1=25, so n=12n=12. The integers are 1212 and 1313.

4. A rectangle has width ww and length w+2w+2. 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

2w+2(w+2)=282w+2(w+2)=28, so 4w=244w=24 and w=6w=6. Length 88 cm.

5. A club charges £4 to join and £3 per visit. The total is £25. Find the visits.

Hint

Let vv be the visit count.

Next step

Try the first operation or write the equation before opening the full solution.

Full working

Equation 4+3v=254+3v=25, so 3v=213v=21 and v=7v=7.

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