Types of Solutions


This Lesson will be relatively brief. We will learn what different outcomes of solutions mean about those equations. There are no questions and it is all theoretical.

Rules of Equation Solution Outcomes

If you solve an equation and end up with; x = a number, then that is a solution, and the equation has a solution.

For example, you solve,

2x + 4 = 8

2x + 4 - 4 = 8 - 4

2x = 4

2x / 2 = 4 / 2

x = 2

Therefore, the equation has a solution

A number = a different number (e.g. 3=7) there are no solutions to the equations

For example, you solve,

2x + 5 = 2x - 7.

2x + 5 - 2x = 2x - 7 - 2x

5 = 7

Therefore, there is no solution to this equation

A number = the same number, (e.g. 5=5) then there are infinite solutions, every value of the variable is a solution to the equation

You solve 3(2x + 3) = 6x + 9

6x + 9 = 6x + 9

6x + 9 - 6x = 6x + 9 - 6x

9 = 9,

Therefore, there are infinite solutions