Question

Solve for x: |x + 9| = 17
A. {8, 26}
B. {8, -26}
C. {-8, 26}
D. {-8, -26}

Answer 1

First break |x + 9| up as a piece-wise defined function:

1.) |x + 9| equals x + 9 when x + 9 ≥ 0.
2.) |x + 9| equals -(x + 9) when x + 9 < 0.


Now that you've set a range, you can get rid of the absolute value and solve for x in both cases:

1.) x + 9 = 17 → x = 17 - 9 → x = 8
2.) -(x + 9) = 17 → -x - 9 = 17 → -x = 26 → x = -26


Your solutions are 8 and -26, which is B.

Answer 2

x+9=17 , x+9=-17
x=8 , x=-26
the answer is B. {8, -26}