Solve the absolute value equation

What is the complete solution of the equation
|8 - 4x| = 40 ?

A.) x = 8 or x = 12
B.) x = 8 or x = -12
C.) x = -8 or x = -12
D.) x = -8 or x = 12
E.) x = -8

Absolute value is the distance away from zero.

This equation shows that (8 - 4x) is 40 away from zero. The two numbers that are 40 away from zero are 40 and -40.
​Therefore, (8 - 4x) could be 40, or (8 - 4x) could be -40.

|8 - 4x| = 40
8 - 4x = 40 or 8 - 4x = -40 {set (8 - 4x) equal to 40 and -40}
-4x = 32 or -4x = -48 {subtracted 8 from each side of each equation}
x = -8 or x = 12 {divided each side by -4}

D.) x = -8 or x = 12

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