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Middle Years

6.04 Three step equations

Worksheet
Three-step equations
1

Solve the following equations:

a

3 \left( 4 s + 1\right) = - 21

b

3 \left( 2 x + 1\right) = 15

c

2 \left( 3 t - 7\right) = 16

d

- 5 \left( 3 x + 8\right) = - 10

e

2 \left( - 3 g + 7\right) = - 16

f

- 2 \left( 3 x - 5\right) = 28

g

- 3 \left( - 2 h - 5\right) = 33

h

- 3 \left( - 2 x + 7\right) = -45

i

4 \left( 5 x - 1\right) = - 24

j

- 4 \left( 5 x + 6\right) = - 104

k

2 \left( 7 + 2x \right) = 38

l

- 3 \left( 4 - x \right) = - 12

m

5 \left( 2 x - 6 \right) = 100

n

6 \left( 3 x + 15 \right) = -72

o

9 \left( 8 - x \right) = 45

p

10 \left( 7 - 3x \right) = 20

q

20 = 2 \left( 3x + 11 \right)

r

16 = 4 \left(2x + 9\right)

s

18 = 3 \left( 2x + 14 \right)

t

-5 = 5 \left(3x + 1\right)

u

26 = 13 \left( 8 - 4x \right)

v

32 = 8 \left(16 - 5x\right)

2

Ryan attempted to solve the equation 9 \left( 4x - 6 \right) = 18. His working is shown below:

\begin{aligned} 9 \left( 4x - 6 \right) &= 18 \\ 4x - 6 &= 9 \\ 4x &= 15 \\x &= \dfrac{15}{4} \end{aligned}
a

What was his mistake?

b

Solve the equation correctly.

3

Solve the following equations:

a

3 \left(w + 8\right) + 5 = 44

b

9 \left(x - 7\right) + 8 = 26

c

- 5 \left(g + 4\right) + 9 = - 41

d

- 7 \left(x + 5\right) + 4 = - 17

e

6 \left(q + 1\right) - 5 = - 23

f

4 \left(x + 6\right) - 8 = 48

g

-8 \left(x + 4\right) - 3 = - 59

h

- 2 \left(x - 2\right) - 7 = - 29

i

2 \left(x - 9\right) - 4 = 16

j

5 \left(x - 3\right) - 7 = - 52

4

Solve the following equations:

a

- \dfrac{y}{3} + 10 = 17

b

- \dfrac{u}{4} + 15 = 8

c

\dfrac{5 x}{8} - 9 = - 4

d

\dfrac{8 c}{3} + 5 = - 11

e

\dfrac{5 x}{3} + 11 = 21

f

\dfrac{- 3 c}{4} + 5 = 14

g

- \dfrac{3 x}{4} + 5 = - 7

h

\dfrac{3 x}{4} - 5 = - 11

i

\dfrac{4 x}{7} - 6 = - 14

j

- \dfrac{5 x}{6} - 6 = 14

5

Solve the following equations:

a

\dfrac{x - 9}{5} + 4 = 7

b

\dfrac{x - 3}{5} - 8 = - 7

c

\dfrac{x + 2}{3} - 25 = - 22

d

\dfrac{x + 16}{3} + 5 = 3

e

\dfrac{2 x - 12}{3} = 0

f

\dfrac{3 x + 6}{2} = 15

g

\dfrac{8 x + 4}{5} = - 4

h

\dfrac{- 3 t - 6}{7} = - 3

i

\dfrac{- 13 - 4 r}{3} = - 15

j

\dfrac{- 9 + 5 x}{2} = - 22

6

Solve the following equations:

a
\dfrac{2\left(x - 4 \right)}{3}=8
b
\dfrac{5\left(x +1 \right)}{2}=10
c
\dfrac{-3\left(x -3 \right)}{4}=0
d
\dfrac{6\left(x +5 \right)}{7}=12
e
\dfrac{9\left(x +10 \right)}{2}=-6
f
\dfrac{4\left(x - 2 \right)}{3}=-3
g
\dfrac{7\left(x - 9 \right)}{5}=14
h
\dfrac{2\left(x +11 \right)}{9}=8
7

Solve the following equations:

a
2\left( \dfrac{x}{3} + 1 \right) = 6
b
5\left( \dfrac{x}{2} + 7 \right) = 60
c
4\left( \dfrac{x}{5} - 3 \right) = -12
d
3\left( \dfrac{x}{4} - 10 \right) = 15
e
18 = 2\left( \dfrac{x}{5} - 7 \right)
f
40 = 10\left( \dfrac{x}{6} - 1 \right)
g
8\left(4 + \dfrac{x}{2} \right) = 48
h
-4\left(12 - \dfrac{x}{3} \right) = -64
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