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

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.