1. One Answer, No Answers, or an Infinite Number of Answers

2. There are three possible forms for the answers of an equation… 1. x = a (Where a is a number) 2. c ≠ d (c and d are numbers) 3. b = b (where b is a number)

3. If when you solve the equation you end up with x equaling a number, then there is only one answer. It is the value of x.

4. Example #1 3(5x – 5) = -75 15x – 15 = -75 15x = -60 x = -4 There is only one solution, -4.

5. If when you solve the equation you end up with an untrue statement such as 4 = 9, then there is no solution to the equation.

6. Example #2 4(7x – 1) = 7(4x + 3) 28x – 4 = 28x + 21 -4 = 21 There are no solutions to this equation because -4 does not equal 21.

7. If when you solve the equation you end up with the same number on both sides of the equation, then there is an infinite number of solutions to the equation.

8. Example #3 4(6x + 2) + 1 = 3(8x + 3) 24x + 8 + 1 = 24x + 9 24x + 9 = 24x + 9 9 = 9 There are an infinite number of solutions to this equation. In other words any number you choose will make this equation true.