Question

solve |x - 4| + 6 = 17. a. x = -15 and x = -7 b. x = 15 and x = -15 c. x = 15 and x = -7 d. x = -15 and x = 7

Explanation:

Step1: Isolate the absolute value

Subtract 6 from both sides:
$|x-4| = 17 - 6$
$|x-4| = 11$

Step2: Split into two cases

Case 1: $x-4 = 11$
Case 2: $x-4 = -11$

Step3: Solve Case 1

Add 4 to both sides:
$x = 11 + 4$
$x = 15$

Step4: Solve Case 2

Add 4 to both sides:
$x = -11 + 4$
$x = -7$

Answer:

C. $x=15$ and $x=-7$