To solve the inequality \( |8x - 8| < 24 \), we can break it into two separate inequalities because of the absolute value:

### Step 1: Set up the two inequalities
1. \( 8x - 8 < 24 \)
2. \( -(8x - 8) < 24 \)

### Step 2: Solve the first inequality
\[ 8x - 8 < 24 \]

Add 8 to both sides:
\[ 8x < 32 \]

Now, divide both sides by 8:
\[ x < 4 \]

### Step 3: Solve the second inequality
\[ -(8x - 8) < 24 \]

Distribute the negative sign:
\[ -8x + 8 < 24 \]

Subtract 8 from both sides:
\[ -8x < 16 \]

Now, divide by -8, and remember to reverse the inequality sign because we are dividing by a negative number:
\[ x > -2 \]

### Step 4: Combine the results
The solution is:
\[
-2 < x < 4
\]

Thus, the solution is \( x \in (-2, 4) \).

Would you like further clarification or more details?

Here are 5 related questions for practice:
1. Solve \( |5x + 3| \leq 10 \).
2. Solve \( |2x - 7| > 3 \).
3. Solve \( 3|x - 2| \leq 12 \).
4. Solve \( |x + 5| \geq 8 \).
5. Solve \( |4x + 1| < 9 \).

**Tip**: When solving absolute value inequalities, always remember to break them into two separate inequalities, considering both the positive and negative cases!

Learn how to solve the absolute value inequality |8x - 8| < 24 with a detailed step-by-step guide. This problem involves key algebraic concepts like absolute value and inequalities. Suitable for students in Grades 9-10.

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