Algebra: Creating and Solving Equations for Word Problems

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.