Math Snap

STEP 1

1. The equation involves an absolute value, which can result in two cases.
2. We need to solve for $x$ and then find the positive value of $x - 1$.

STEP 2

1. Set up the two cases for the absolute value equation.
2. Solve each case for $x$.
3. Determine the positive value of $x - 1$.

STEP 3

The absolute value equation $|4x - 4| = 112$ can be split into two separate equations:
Case 1: $4x - 4 = 112$
Case 2: $4x - 4 = -112$

STEP 4

Solve Case 1: $4x - 4 = 112$
Add 4 to both sides:
$$4x - 4 + 4 = 112 + 4$$ $$4x = 116$$ Divide by 4:
$$x = \frac{116}{4}$$ $$x = 29$$

STEP 5

Solve Case 2: $4x - 4 = -112$
Add 4 to both sides:
$$4x - 4 + 4 = -112 + 4$$ $$4x = -108$$ Divide by 4:
$$x = \frac{-108}{4}$$ $$x = -27$$

We need the positive value of $x - 1$.
For $x = 29$:
$$x - 1 = 29 - 1$$ $$x - 1 = 28$$ For $x = -27$:
$$x - 1 = -27 - 1$$ $$x - 1 = -28$$ The positive value of $x - 1$ is:
$$\boxed{28}$$