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.