OG详解-OG1 数学2 Q21

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 , 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.