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

Question

Accepted Answer

The correct answer is 28 . The given absolute value equation can be rewritten as two linear equations: 4 x - 4 = 112 and - 4 x - 4 = 112 , or 4 x - 4 = - 112 . Adding 4 to both sides of the equation 4 x - 4 = 112 results in 4 x = 116 . Dividing both sides of this equation by 4 results in x = 29 . Adding 4 to both sides of the equation 4 x - 4 = - 112 results in 4 x = - 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 .

Question if-4-x