The main purpose of algebra is to solve problems.

Using equations to solve problems can be useful when we are given a word problem.

**Example**

I think of a number and multiply it by 6. After adding 20 to the result, my answer is 2. What is the number I first thought of?

Let the number I first thought of be x

When I multiply by 6 and add 20, this becomes 6x + 20. This is equal to 2.

The equation is: ** 6x + 20 = 2**

Solve to get:

6x = -18

x = -3

**The number I first thought of is -3**

We can check our answer by putting it back into the equation:

-3 × 6 = -18

-18 + 20 = 2 so it works.

Let's have a go at some questions now.