https://file.aiquickdraw.com/mathbot/file/1726625745215obwybgdz.jpg

The equation given in the image is:

\[
|4x - 4| = 112
\]

To find the positive value of \( x - 1 \), let's solve this step by step:

### Step 1: Remove the absolute value

The absolute value equation \( |A| = B \) means that \( A = B \) or \( A = -B \). So, we can split the equation into two cases:

1. \( 4x - 4 = 112 \)
2. \( 4x - 4 = -112 \)

### Step 2: Solve each case

**Case 1:**

\[
4x - 4 = 112
\]
Add 4 to both sides:

\[
4x = 116
\]
Divide by 4:

\[
x = 29
\]

**Case 2:**

\[
4x - 4 = -112
\]
Add 4 to both sides:

\[
4x = -108
\]
Divide by 4:

\[
x = -27
\]

### Step 3: Find \( x - 1 \)

Now, calculate \( x - 1 \) for both solutions.

- If \( x = 29 \), then:
  \[
  x - 1 = 29 - 1 = 28
  \]
  
- If \( x = -27 \), then:
  \[
  x - 1 = -27 - 1 = -28
  \]

### Conclusion

The positive value of \( x - 1 \) is \( 28 \).

---

Would you like further details or have any questions about this solution?

Here are 5 questions to further your understanding:
1. How do we interpret absolute value equations?
2. What other methods can be used to solve absolute value equations?
3. Can this problem have more than two possible values for \( x \)?
4. How does shifting by a constant (like \( -4 \) here) affect the solution?
5. What are the implications of solving equations with negative results?

**Tip:** Always check both possible solutions in an absolute value equation to ensure all cases are covered.

If |4x - 4| = 112, what is the positive value of x - 1?

Learn how to solve the absolute value equation |4x - 4| = 112 and find the positive value of x - 1. This problem involves key algebraic concepts like absolute values and linear equations. Suitable for students in Grades 8-10.

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