Answer: The solutions to the equation 2|2x - 2| + 4 = 20 are x = 5 and x = -3
Explanation:
Step 1: Subtract 4 from both sides of the equation:
2|2x - 2| = 16
Step 2: Divide both sides of the equation by 2:
|2x - 2| = 8
Step 3: We now have two cases to consider since the absolute value can result in two possible solutions:
Case 1: 2x - 2 = 8
Solve for x:
2x = 8 + 2
2x = 10
x = 10/2
x = 5
Case 2: -(2x - 2) = 8
Solve for x:
-2x + 2 = 8
-2x = 8 - 2
-2x = 6
x = 6/(-2)
x = -3
Therefore, the solutions to the equation 2|2x - 2| + 4 = 20 are x = 5 and x = -3