Page 101 - MAT KS3 Y8 Cambridge CheckPoint

9.3 Constructing and solving equations

9.3 Constructing and solving equations

When you are given a problem to solve, you may need to construct, or write, an equation to help you
solve the problem.

Worked example 9.3
3(x + 3) cm
The diagram shows a rectangle.
5y – 4 cm 3y + 8 cm
Work out the values of x and y.
24 cm

3(x + 3) = 24 The two lengths must be equal, so construct an equation by writing one
length equal to the other.
3x + 9 = 24 The first step is to multiply out the brackets.
3x + 9 − 9 = 24 − 9 Use inverse operations to solve the equation. Start by subtracting 9 from
both sides.
3x = 15 Simplify both sides of the equation.
15
x = , Divide 15 by 3 to work out the value of x.
3
x = 5
5y − 4 = 3y + 8 The two widths must be equal, so write one width equal to the other.
5y − 4 − 3y = 3y + 8 − 3y Rewrite the equation by subtracting 3y from both sides.
2y − 4 = 8 Simplify.
2y − 4 + 4 = 8 + 4 Use inverse operations to solve the equation. Start by adding 4 to
both sides.
2y = 12 Simplify both sides of the equation.
12
y = , Divide 12 by 2 to work out the value of y.
2
y = 6

✦ Exercise 9.3

1 Work out the value of x and y in each of these diagrams. All measurements are in centimetres.

a 5x – 3 b 3x + 1 c 5x – 3

2(y + 3) 20 4y + 5 2y + 15 3y + 16 8y – 4
37 2(x + 5) 3x + 11

d 25 e 3x f 6(x + 1)

16 8(y – 1) 5y + 1 16
2(y + 3) 20
5 + 4x 18
72

9 Simplifying expressions and solving equations 99