Answer: x < -2 or x > 6.
Step-by-step explanation: To solve the absolute value inequality |2x - 4| > 8, we need to consider two cases:
Case 1: 2x - 4 > 0
If 2x - 4 > 0, then we can simplify the inequality as follows:
|2x - 4| > 8
2x - 4 > 8 or 2x - 4 < -8
Solving the first inequality, we get:
2x - 4 > 8
2x > 12
x > 6
Solving the second inequality, we get:
2x - 4 < -8
2x < -4
x < -2
Therefore, the solution to the inequality when 2x - 4 > 0 is x < -2 or x > 6.
Case 2: 2x - 4 < 0
If 2x - 4 < 0, then we can simplify the inequality as follows:
|2x - 4| > 8
-(2x - 4) > 8 or -(2x - 4) < -8
Solving the first inequality, we get:
-(2x - 4) > 8
-2x + 4 > 8
-2x > 4
x < -2
Solving the second inequality, we get:
-(2x - 4) < -8
-2x + 4 < -8
-2x < -12
x > 6
Therefore, the solution to the inequality when 2x - 4 < 0 is x < -2 or x > 6.
Combining the solutions from both cases, we get:
x < -2 or x > 6