# Solving Equations

An equation tells us that two things are equal.
To solve an equation we need to find out what a missing number is.

Here is an equation:

a + 9 = 15

a is a missing number. To solve this equation we need to work out what number a is.

Because both sides of the equation are equal if we do the same thing to both sides the equation will still be equal.

At the moment we have 9 added onto a. To get a by itself we can do the opposite of adding 9, subtracting 9. If we subtract 9 from both sides of the equation we have:

a + 9 - 9 = 15 - 9
a = 6

We have solved the equation and found that a = 6

Example 1:
Solve: b - 12 = 8

We can add 12 to both sides of the equation to get b by itself

b - 12 + 12 = 8 + 12
b = 20

Example 2:
Solve: 5c = 45

5c means 5 × c
The opposite of multiplying by 5 is dividing by 5
To get c by itself we can divide both sides by 5.

5c5 = 455
c = 9

Example 3:
Solve: d3 = 12

5c means 5 × c
The opposite of dividing by by 3 is multiplying by 3
To get d by itself we can multiply both sides by 3.

3d3 = 12 × 3
d = 36

Try these: