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Unit F2 Section 2
Simple Equations

To solve simple equations you must carry out the same operation (addition, subtraction, multiplication or division) on both sides of the equation so that the new equation is still balanced.

Worked Examples

1

Solve each of the following equations.

(a)

x + 3 = 8

To solve this equation, subtract 3 from both sides.

x + 3 = 8
x + 3 − 3 = 8 − 3
x = 5
(b)

x − 8 = 11

To solve this equation, add 8 to both sides.

x − 8 = 11
x − 8 + 8 = 11+ 8
x = 19
(c)

4x = 32

To solve this equation divide both sides by 4.

4x = 32
=
x = 8
(d)

= 7

To solve this equation multiply both sides by 6.

= 7
× 6 = 7 × 6
x = 42
2

A packet of sweets is divided equally among 5 children and each child is given 4 sweets. Write down an equation to describe this situation and solve it to find the number of sweets in the packet.

Let x be the number of sweets in the packet.

Then

= 4

since the 5 children have 4 sweets each. Now the equation can be solved by multiplying both sides by 5.

× 51 = 4 × 5
x = 20

Exercises

Solve each of these equations.

(a)
x + 6 = 10 x =
(b)
x − 7 = 3 x =
(c)
x + 4 = 7 x =
(d)
x − 1 = 11 x =
(e)
x − 6 = 8 x =
(f)
x + 5 = 3 x =
(g)
5x = 45 x =
(h)
6x = 24 x =
(i)
6x = 108 x =
(j)
7x = 56 x =
(k)
3x = 102 x =
(l)
6x = 42 x =
(m)
= 5 x =
(n)
= 12 x =
(o)
= 10 x =
(p)
= 4 x =
(q)
= 3 x =
(r)
= 11 x =
(s)
x − 5 = 3 x =
(t)
x + 8 = 14 x =
(u)
4x = 104 x =
(v)
= 18 x =
(w)
x − 3 = 12 x =
(x)
x + 7 = 11 x =

Solve each of these equations.

(a)
x + 6 = 2 x =
(b)
x + 8 = 3 x =
(c)
x − 5 = −2 x =
(d)
x + 2 = −4 x =
(e)
x − 2 = −6 x =
(f)
x + 4 = −10 x =
(g)
2x = −12 x =
(h)
3x = −24 x =
(i)
5x = −60 x =
(j)
= −8 x =
(k)
x − 2 = −5 x =
(l)
x + 6 = −14 x =
(m)
x − 10 = −2 x =
(n)
x − 12 = −4 x =
(o)
x − 7 = −1 x =
(p)
x + 4 = −1 x =
(q)
x + 12 = 2 x =
(r)
x + 10 = −16 x =

The angles on a straight line add up to 180°. Solve an equation for each diagram shown below.

(a)
x = °
(b)
x = °
(c)
x = °
(d)
x = °

To pay for a school trip, 12 students take the same amount of money to school. If the total money collected is £54 and the amount each students takes is x, write down an equation to describe this situation. Solve your equation for x.

x = £

The cost of a journey increases by £3 to £41. If x is the original cost, write down an equation to describe this situation. Solve your equation for x.

x = £

Grace is twice as old as Carla. Carla is 2 years younger than George. George is 11 years old.

(a)

How old is Carla?

years old
(b)

How old is Grace?

years old