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

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The correct answer is 28. The given absolute value equation can be rewritten as two linear equations: 4x − 4 = 112 and −(4x − 4) = 112, or 4x − 4 = −112. Adding 4 to both sides of the equation 4x − 4 = 112 results in 4x = 116. Dividing both sides of this equation by 4 results in x = 29. Adding 4 to both sides of the equation 4x − 4 = −112 results in 4x = −108. Dividing both sides of this equation by 4 results in x = −27. Therefore, the two values of x − 1 are 29 − 1, or 28, and −27 − 1, or −28. Thus, the positive value of x − 1 is 28. Alternate approach: The given equation can be rewritten as 4|x − 1| = 112. Dividing both sides of this equation by 4 yields |x − 1| = 28. This equation can be rewritten as two linear equations: x − 1 = 28 and −(x − 1) = 28, or x − 1 = −28. Therefore, the positive value of x − 1 is 28.

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