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CanadaON
Grade 8

3.05 Solving equations

Worksheet
One-step equations
1

For each of the following equations, describe what must be done to both sides in order to solve the equation:

a

x - 4 = 6

b
x - 2 = 9
c
4x = 92
d
\dfrac{x}{5} = 7
e
x + \dfrac{1}{5} = \dfrac{3}{5}
f
x - \dfrac{5}{8} = \dfrac{1}{8}
g
4n = 28
h
36= 9n
2

For each of the following equations:

i

Describe how to make the variable the subject of the equation.

ii

Solve the equation.

a
y + 5 = 9
b
t - 2 = 35
c
9 p = 36
d
\dfrac{n}{12} = 11
e
y + 3 = -8
f
t - 3 = -45
g

5 p = - 50

h

- \dfrac{n}{9} = 4

3

Solve the following equations:

a
x - 4 = 10
b
3 x = 18
c
4 k = 20
d
8 k = 56
e

8 k = - 48

f

- 7 m = 63

g

5 m = 11

h
n + 27 = 11
i
6 = - 16 + n
j
4n = 20
k
88 = 11n
l
59n= 177
m

p + 36 = 62

n

24 + p = - 2

o
q + 8 = 10
p
r + 22 = 69
q
s + 8 = 29
r
s-23 = -25
s
t - 15 = 0
t
9 t = 3
u

\dfrac{t}{5} = 1.6

v

v + 41 = 4

w
v - 4 = 44
x
- 5 = \dfrac{v}{5}
y
\dfrac{q}{7} = 6
z

\dfrac{q}{5} = - 4

Two-step equations
4

Use substitution to determine whether the given value of x is the solution to each equation:

a

x - 10 = - 1 where x = 9

b

x - 4 = - 5 where x = 0

c

x + 1 = 7 where x = 6

d

x - 3 = - 3 where x = 3

e

8 x = 51 where x = 6

f

2 x = 8 where x = 4

g

3 x + 1 = 7 where x = 2

h

6 x - 13 = 12 where x = 4

i

5 x + 12 = 31 where x = 4

j

4 x - 2 = 18 where x = 5

k

\dfrac{x}{2} = 8 where x = 19

l

\dfrac{x}{3} = 8 where x = 24

5

Solve the following equations:

a

3 x + 11 = 5

b
4 x - 6 x = 4
c
- 10 + 3 k = 5
d
8 m + 9 = 65
e

12 q + 8 = 26

f

4 s - 9 = 39

g

- 6 s + 5 = 47

h

6 t + 2 = - 22

i
- w - 7 = 7
j
5 w - 8 = 2
k
- 63 - 9 y = 63
6

Solve the following equations:

a

\dfrac{5 x}{6} = 11

b

\dfrac{x + 15}{2} = 5

c

\dfrac{4n}{9} = 10

d

\dfrac{x}{7} + 13 = 21

e

\dfrac{m - 6}{4} = 4.25

f

\dfrac{n + 36}{2} = 11

g

\dfrac{x}{7} + 19 = 16

h

\dfrac{- 44}{p} = 11

i

\dfrac{4}{q} = 28

j

\dfrac{30}{q} = - 5

k

\dfrac{r - 6}{4} = - 6

l
\dfrac{v}{7} + 3 = - 1
m

\dfrac{w}{2} + 14 = 6

n
\dfrac{-125}{w} = -25
7

Solve the following equations:

a

2 \left(q + 11\right) = 20

b

3 \left(q + 3\right) = - 18

c

2 \left(p + 6\right) = - 8

d

7 \left(11 - n\right) = 210

e

- 4 \left(r + 5\right) = - 44

f

2 \left(u + 2\right) = - 8

g

2 \left(u + 5\right) = 18

h

4 \left(u - 4\right) = - 36

i
5 \left(u + 1\right) = 25
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8.C2.3

Solve equations that involve multiple terms, integers, and decimal numbers in various contexts, and verify solutions.

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