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Middle Years

7.06 Solving further equations

Worksheet
Two-step equations
1

Solve the following equations, remembering to check your answer:

a
2 w + 9 = 37
b
5 n + 35 = 15
c

7 x + 17 = 45

d
2 x + 13 = 19
e

4 x + 9 = 25

f

2 t + 13 = 35

g

7 m + 18 = 39

h

12 p + 3 = 51

i

2x + 14 = 20

j

6y + 4 = 34

k

3q + 9 = 12

l

-9 n + 8 = -55

m

- 5 t + 27 = 17

n

8u + 12 = -12

o

11x + 38 = 27

p

7y + 38 = 3

2

Solve the following equations:

a
6 m - 66 = - 12
b
8q - 42 = - 10
c

13 x - 2 = 24

d

5 t - 15 = 15

e

29 m - 8 = 21

f

11 x - 22 = 22

g

2p - 17 = 3

h

9q - 4 = 23

i

6n - 29 = 7

j

-7s - 23 = 19

k

12m - 7 = -19

l

-4x - 29 = -13

Equations with fractions and brackets
3

Solve the following equations:

a
\dfrac{x}{5} + 3 = 11
b
\dfrac{j}{8} - 17 = - 13
c
\dfrac{k}{8} - 13 = - 6
d
\dfrac{r}{6} - 3 = 4
e

\dfrac{x}{3} + 2 = 7

f

\dfrac{q}{2} + 18 = 25

g

\dfrac{s}{7} + 14 = 5

h

\dfrac{m}{5} + 13 = 22

i

\dfrac{p}{11} - 3 = 3

j

\dfrac{n}{8} - 5 = 4

k

\dfrac{p}{13} - 11 = -7

l

\dfrac{x}{12} + 2 = -6

m

\dfrac{s}{4} + 15 = 31

n

\dfrac{x}{6} + 25 = 17

o
\dfrac{t}{2} + 6 = -8
p
\dfrac{m}{2} + 11 = 16
4

Solve the following equations:

a
\dfrac{u + 7}{2} = 5
b
\dfrac{q - 10}{4} = - 6
c
\dfrac{m + 11}{2} = 10
d

\dfrac{47 + m}{15} = 3

e

\dfrac{r+11}{5} = 7

f

\dfrac{m+26}{17} = 3

g

\dfrac{t-5}{4} = 8

h

\dfrac{q-17}{3} = -4

5

Solve the following equations:

a
5 \left(t + 9\right) = 60
b
4 \left(x + 5\right) = 20
c
2 \left(p + 14\right) = 58
d
3 \left(p + 9\right) = 48
e

9 \left( x + 2 \right) = 27

f

2 \left( p + 9 \right) = 28

g

6 \left( x + 5 \right) = 54

h
3\left(n + 5\right) = 24
i
4 \left(k - 4\right) = 48
j
3 \left(s - 16\right) = - 21
k
9 \left(p - 3\right) = 0
l
2 \left(l - 12\right) = - 10
m
4 \left(s - 29\right) = 4
n
4 \left(s - 8\right) = 16
o
3\left(s - 9\right) = 3
p

13 \left( s - 7 \right) = 143

Mixed equations
6

Solve the following equations:

a
\dfrac{8 t}{3} = 16
b
-13 = 7z-48
c
\dfrac{3 y}{8} = -6
d

11 - \dfrac{x}{6} = 9

e

14 = 3 r - 7

f
48 = 6 \left(p+8\right)
g

3 \left( 12 - x \right) = 90

h

\dfrac{-2 + n}{6} = -15

i
6 = \dfrac{t}{5} - 3
j

17 - 8 s = -7

k
4 = 4 \left(s - 29\right)
l

8\left( 2 + s \right) = -32

m

10 = 2x + 6

n

-15 -5x = 10

o
7 - \dfrac{x}{2} = 9
p

11 = \dfrac{x+1}{2}

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