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.

Learn how to solve the absolute value equation |4x - 4| - 8 = -3 through a step-by-step solution. This problem introduces concepts related to absolute value properties and involves solving for multiple cases. Ideal for students in Grades 8-10.

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