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Math  /  Algebra

QuestionIf ∣4x−4∣=112|4 x-4|=112, what is the positive value of x−1x-1 ?

Studdy Solution

STEP 1

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

STEP 2

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

STEP 3

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

STEP 4

Solve Case 1: 4x−4=112 4x - 4 = 112
Add 4 to both sides:
4x−4+4=112+4 4x - 4 + 4 = 112 + 4 4x=116 4x = 116
Divide by 4:
x=1164 x = \frac{116}{4} x=29 x = 29

STEP 5

Solve Case 2: 4x−4=−112 4x - 4 = -112
Add 4 to both sides:
4x−4+4=−112+4 4x - 4 + 4 = -112 + 4 4x=−108 4x = -108
Divide by 4:
x=−1084 x = \frac{-108}{4} x=−27 x = -27

STEP 6

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

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