We are given the equation:

$|4x - 4| - 8 = -3$

Let's solve this step by step.

Step 1: Isolate the absolute value term

Add 8 to both sides to eliminate the -8:

$|4x - 4| = -3 + 8$ $|4x - 4| = 5$

Step 2: Remove the absolute value by considering two cases

The absolute value equation $|4x - 4| = 5$ gives us two possible cases:

Case 1: $4x - 4 = 5$

Solve for $x$: $4x = 5 + 4$ $4x = 9$ $x = \frac{9}{4}$

Case 2: $4x - 4 = -5$

Solve for $x$: $4x = -5 + 4$ $4x = -1$ $x = \frac{-1}{4}$

Step 3: Final answer

The two possible solutions are:

$x = \frac{9}{4} \quad \text{or} \quad x = \frac{-1}{4}$

Do you want further details or have any questions?

Here are 5 related questions for practice:

1. Solve $|3x - 2| - 7 = 4$.
2. Solve $|2x + 1| + 5 = 10$.
3. What is the solution to $|5x + 7| = 13$?
4. Solve $|x - 1| - 6 = 0$.
5. Solve $|2x - 3| = 7$.

Tip: When solving absolute value equations, always remember to consider both positive and negative cases.