Question

Solve for x: |-4x + 20| + 4 = 12

a) x = -1
b) x = 6
c) x = 3
d) x = 4

Answer 1

The solution to the equation |-4x + 20| + 4 = 12 involves isolating the absolute value, creating two separate equations, and solving for x, resulting in x = 3 and x = 7; however, only x = 3 is an available answer choice.

Step-by-step explanation:

To solve the equation |-4x + 20| + 4 = 12, we first isolate the absolute value expression:

Subtract 4 from both sides: |-4x + 20| = 8.The absolute value equation |-4x + 20| = 8 can split into two separate equations: -4x + 20 = 8 and -4x + 20 = -8.Solving the first equation for x: Solving the second equation for x:The solutions to the equation are x = 3 and x = 7. However, since x = 7 is not an option in the given choices, the correct answer from the options provided is x = 3 (c).