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iGCSE (2021 Edition)

6.05 Variables on both sides

Worksheet
Equations with variables on both sides
1

Explain what should be done to solve the equation 9 x = 7 + 8 x.

2

Solve the following equations:

a

7 x + 6 = 3 x + 22

b

6 x - 3 = 4 x + 7

c

5 x - 3 = - 4 x + 33

d

4 x - 9 = 5 x - 6

e

7 x = x + 30

f

3 x = x - 18

g

8 x = 6 x + 10

h

7 x = 3 x - 12

i

3 x = - 8 x - 44

j

10 x +8= - 8 x - 2

k

5x + 7= 3 x + 11

l

11x + 15= 6 x + 35

m

6x - 5= 3 x + 22

n

-4x +10= 2 x + 8

o

16+4x = 12 x

p

18-2x = 9 + x

q

24-6x = 14 + 4x

r

30-10x = 22 - 8x

3

Solve the following equations:

a
5x+7 - 3x=x-10
b
8x+6 - 2x=4x+8
c
9x+8 +2x=3x-16
d
10x+12 - 2x=6x+8-4x
4

Solve the following equations:

a

5 \left( 2 x + 5\right) =2x + 13

b

6 \left( 3 x + 1\right) =4x + 20

c

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

d

2 \left(8 - 3 x\right) =10x - 20

e

3 x + 4 = 5 \left( 6 x + 5\right) + 60

f

3 x + 4 = 6 \left( 5 x - 5\right) + 88

g

4 x - 6 = - 8 \left( 6 x - 7\right) + 42

h

8 \left( 8 x + 5\right) = 3 \left( 6 x + 8\right) + 108

i

5 \left( 4 x - 3\right) = 3 \left( - 4 x + 4\right) + 101

j

- 5 \left( - 5 x + 5\right) = 7 \left( 4 x - 8\right) + 37

5

Solve the following equations:

a
2\left( 3x+4 \right) + 5\left( x - 3 \right) = 6\left(x+10\right)
b
5\left( 2x+1 \right) - 3\left( 3x - 1 \right) = 2\left(x+1\right)
c
8\left( 2x - 5 \right) - 3x = 10 - 5\left( x + 9 \right)
d
2 - 6\left( 2x+1 \right) = 4\left( 3x - 1 \right) + 6\left(x+10\right)
e
2\left( 3x+5 \right) - \left( 3x - 9 \right) = 7 - 2\left(3x+12\right)
f
4\left( 5x+8 \right) + 2\left( 3x - 5 \right) = 7\left(x+11\right) - \left(2x-8 \right)
6

Solve the following equations:

a

\dfrac{4 x - 40}{8} = 3 x

b

\dfrac{4 x + 84}{8} = - 3 x

c

\dfrac{- 6 x + 54}{4} = 3 x

d

\dfrac{3 x + 6}{7} = x + 2

e

\dfrac{- 7 x + 7}{3} = 6 x + 19

f

\dfrac{5 x - 6}{7} = - 5 x + 22

g

\dfrac{4 x + 6}{6} = \dfrac{3 x + 12}{7}

h

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

i

\dfrac{4 x + 8}{8} = \dfrac{- 3 x + 12}{3}

j

\dfrac{8 x - 2}{9} = \dfrac{6 x - 4}{7}

7

Consider the equation 3 k + 4 = A k - 2. If k = 6 in this equation, find the value of A.

Applications
8

A number is multiplied by 5 and then 2 is added. Then the results is multiplied by 6. This is equal to 10 times the number minus 8.

a

Form an equation for this problem.

b

Solve the equation to find the number.

9

A rectangle with a height of 3x + 7 \text{ cm} and a width of 4x has the same perimeter as a square with side length 2x+9\text{ cm}.

Find the value of x.

10

A square with side length 4x - 11 \text{ cm} has the same perimeter as a square with side length 2x+9\text{ cm}.

Find the value of x.

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Outcomes

0607C2.3

Solution of linear equations.

0607E2.3

Solution of linear equations including those with fractional expressions.

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