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13.1 Solving linear equations

7 Solve these equations.
a 4(2p + 3) = 16 b 4(2p − 3) = 16 c 4(2p + 3) = 16p d 4(2p − 3) = 16p
8 Solve these equations. Give the answers as fractions.
a 3x + 12 = 20 − 4x b 9(2 + 3y) = 39 c z + 15 = 5(7 − z) )
+ 15 = 5(7 −
9 Look at Shen’s homework. 2(x + 8) = 3(6– x)
There is a mistake on each line of his solution.
Copy out his working and correct the mistakes. A 2x + 8 = 18–3x
A –x + 8 = 18

A x = 26
10 Here is an equation.
10(x − 4) = 5x + 25
a Jake starts to solve it by multiplying out the brackets. He writes: 10x – 40 = 5x + 25
Complete Jake’s solution.
b Zalika starts to solve it by dividing both sides of
10(x − 4) = 5x + 25 by 5.
Complete Zalika’s solution.
c Whose method is better?
11 Dakarai and Mia start to solve the equation 6 − 2x = 3x + 25.

Dakarai writes: 6 – 2x = 3x + 25 Mia writes: 6 – 2x = 3x + 25
A 6 = 5x + 25 A –2x = 3x + 19

A A

a What does Dakarai do first?

b Complete Dakarai’s solution.
c What does Mia do first?

d Complete Mia’s solution.
12 The equations and the answers below are mixed up.
Copy the equations and the answers, like this.
2(x + 3) + x = 0 x = 8
x + 2(x − 3) = 0 x = 6
3x − 2(x + 3) = 0 x = 2
−(x + 2) + 2(x − 3) = 0 x = 1
x − (2 − x) = 0 x = −2
Draw a line from each equation to the correct answer.

13 Solve these equations.
a 12 − (m − 3) = 4 b 12 − (3 − m) = 4 c 12 − 2(m − 3) = −4

14 Solve these equations.
a x + 2(x + 1) + 3(x + 2) = 4(x + 3)
b x + 2(x − 1) − 3(x − 2) = 4(x − 3)

126 13 Equations and inequalities