Short Answer 
The absolute value equation |4x + 4| = 112 leads to two cases: Case 1 gives x = 27 and Case 2 gives x = -29. Evaluating x – 1 results in 26 for x = 27 and -30 for x = -29, with the positive result being 26.
Step 1: Set Up the Absolute Value Cases
Begin by recognizing that the absolute value equation |4x + 4| = 112 gives rise to two distinct scenarios. You need to establish the following cases to solve for x:
- Case 1: 4x + 4 = 112
- Case 2: 4x + 4 = -112
Step 2: Solve Each Case
Now, solve each case to find the possible values of x. For Case 1, subtract 4 from both sides leading to 4x = 108, then divide by 4 to get x = 27. For Case 2, similarly subtract 4 from both sides giving 4x = -116, then divide by 4 leading to x = -29.
Step 3: Calculate x – 1 and Identify the Positive Result
Next, compute the expression x – 1 for both values derived from each case. From x = 27, you get x – 1 = 26. From x = -29, you find x – 1 = -30. Finally, to find the positive value, the result is 26.