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

Explanation

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 4 = - 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, which is equivalent to 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.