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5.03 Distributing to solve

Worksheet
Equations with brackets
1

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

a

x = 6 where 2 \left(x - 3\right) = - 8.

b

x = 8 where 7 \left(x - 6\right) = 14.

c

x = 8 where 3 \left(x - 6\right) = 6.

d

x = 8 where 9 = 7 \left(x - 7\right).

2

Solve the following equations by first expanding the brackets:

a
2 \left(x + 2\right) = 0
b
7 \left(x - 5\right) = 0
c

4 \left(x + 5\right) = 32

d

5 \left(x + 5\right) = 39

e

4 \left(x + 6\right) = - 60

f

12 \left(x + 5\right) = 168

g

3 \left(x - 4\right) = - 21

h

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

i

5 \left( x - 4\right) = -15

j

12 \left(x - 6\right) = 12

k

5 \left( 2 x + 6\right) = 69

l

6 \left( 3 x + 5\right) = 192

m

9 \left( 3 x + 5\right) = 153

n

6 \left( 2 x - 6\right) = - 90

o

6 \left( 3 x - 5\right) = - 102

p

9 \left( 3 x - 5\right) = 63

q

- 6 \left( 4 x + 5\right) = - 143

r

- 6 \left( 3 x + 6\right) = 54

s

- 8 \left( 4 x + 5\right) = 120

t

- 6 \left( 2 x - 4\right) = 81

u

- 6 \left( 4 x - 5\right) = 174

v

- 8 \left( 2 x - 6\right) = - 16

3

Solve the following equations:

a

4 \left( 2 x + 5\right) + 4 = 48

b

6 \left( 4 x + 8\right) - 9 = 87

c

5 \left( 4 x + 5\right) + 3 x = 71

d

4 \left( 2 x - 6\right) - 3 x = 16

e

5 \left( 2 x + 5\right) + 4 x + 6 = 59

f

4 \left( 4 x - 6\right) - 3 x + 8 = 36

g

- 3 \left( 4 x + 7\right) + 3 x - 5 = - 8

h

- 4 \left( 4 x + 7\right) - 3 x + 5 = 15

i

- 3 \left( 4 x + 6\right) - 3 x - 7 = - 70

j

- 4 \left( 4 x + 6\right) + 3 x + 7 = - 56

4

Solve the following equations:

a

4 \left( 3 x + 5\right) + 3 \left( 2 x + 6\right) = 74

b

2 \left( 2 x - 5\right) + 3 \left( 4 x + 6\right) = 56

c

2 \left( 4 x + 5\right) + 3 \left( 3 x - 6\right) = - 42

d

3 \left( 4 x + 6\right) - 2 \left( 3 x + 5\right) = 26

e

5 \left( 4 x - 6\right) - 3 \left( 2 x + 5\right) = - 73

f

8 \left( 4 x + 5\right) - 3 \left( 2 x - 6\right) = - 46

g

- 3 \left( 2 x + 5\right) + 5 \left( 4 x + 6\right) = 57

h

- 3 \left( 2 x + 5\right) + 5 \left( 3 x + 6\right) = 42

i

- 3 \left( 2 x + 6\right) + 5 \left( 4 x - 5\right) = - 15

j

- 3 \left( 2 x - 4\right) + 5 \left( 3 x + 5\right) = 55

k

- 3 \left( 2 x - 6\right) + 5 \left( 4 x - 5\right) = 21

l

- 3 \left( 2 x + 4\right) + 5 \left( 3 x + 5\right) = 40

Applications
5

A square has a side length of \, 4x + 5\text{ cm}. If the perimeter of the square is 44 \text{ cm}, find the value of x.

6

A rectangle has a width of \, 5x-3\text{ cm} and a height of \, 3x + 7\text{ cm}. If the perimeter of the rectangle is 42 \text{ cm}, find the value of x.

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Outcomes

VCMNA284

Solve linear equations using algebraic and graphical techniques. Verify solutions by substitution

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