Solve for all values of x in simplest form. 5-3|2x-7|=-31

x = 9 1/2 x = - 2 1/2

Step-by-step explanation:

5-3|2x-7|=-31

Subtract 5 from each side

5-5-3|2x-7|=-31-5

-3|2x-7|=-36

divide by - 3

-3/-3|2x-7|=-36/-3

|2x-7|=12

There is a positive and negative solution to the absolute value equation

2x-7 = 12 2x - 7 = - 12

Add 7 to each side

2x-7+7 = 12+7 2x-7+7 = - 12+7

2x = 19 2x = - 5

Divide by 2

2x/2 = 19/2 2x/2 = - 5/2

x = 9 1/2 x = - 2 1/2