Topics
7. Equations
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Middle Years

7.03 Solving equations with algebra

Lesson
Worksheet
Practice
Worksheet
Inverse operations
1

Consider the equation 9 p = 36.

a

What operation should be done to make p the subject of the equation?

b

Hence, find the solution.

2

Consider the equation y + 5 = 9.

a

What operation should be done to make y the subject of the equation?

b

Hence, find the solution.

3

Consider the equation y + 3 = -8.

a

What operation should be done to make y the subject of the equation?

b

Hence, find the solution.

4

Consider the equation \dfrac{p}{12} = 11.

a

What operation should be done to make p the subject of the equation?

b

Hence, find the solution.

5

State the operation that should be applied to both sides in order to solve each equation:

a

x - 4.5 = 6.8

b
\dfrac{x}{4.1} = 7.6
c
7 p = -63
d
s - 2 = 35
e
t - 3 = -45
f
4.1 x = 94.3
g
x + \dfrac{1}{5} = \dfrac{3}{5}
h
x - \dfrac{5}{8} = \dfrac{1}{8}
i
x - 1.39 = 8.67
j
4 n = 27.2
k
36.5 = 7.3 n
One-step equations
6

Solve the following equations:

a
x + 3 = 11
b
x + 2 = 15
c
x + 9 = 26
d
10 + x = 19
7

Solve the following equations:

a
x - 10 = 30
b
x - 5 = 12
c
x - 8 = 21
d
x - 4 = 16
8

Solve the following equations:

a
3x = 27
b
2x = 14
c
5x = 25
d
9x = 90
9

Solve the following equations:

a
\dfrac{x}{4} = 5
b
\dfrac{x}{3} = 8
c
\dfrac{x}{2} = 11
d
\dfrac{x}{6} = 8
10

Solve the following equations:

a
q + 8 = 10
b
s + 8 = 29
c
r + 22 = 69
d
u - 3 = 4
e
v - 4 = 44
f
u - 22 = 4
g
4 k = 20
h
8 k = 56
i
\dfrac{r}{5} = 4
j
\dfrac{q}{7} = 6
k
y + 7 = 6
l
24 + p = 59
m
22 - x = 15
n
12 n = 60
o
48 + x = 30
p
22 - x = 41
q
-27 + m = -32
r
s-23 = -25
11

For each word description, find the unknown number:

a

When 10 is added to a number, the result is 12.

b

When a number is multiplied by 10, the result is 60.

c

When 20 is subtracted to a number, the result is 5.

d
When a number is divided by 8, the result is 9.
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