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?

(a) Let the number I first thought of be x.

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

The equation is:

6x + 20 = 2

(d) Solve to get:

6x = -18

x = -3

(e) **The number I first thought of is -3**

(f) -3 × 6 = -18

-18 + 20 = 2 so it works.