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.

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**.