Question

Solve for x: |x + 2| + 16 = 14

1.x=-32and x=-4
2.x=-4and x=0
3.x=0 and x=28
4. no solution

Answer 1

`|x+2|+16=14 \ \ \ \ | subtract\ 16\\\\ |x+2|=-2\\\\ x+2=-2\ \ \ or\ \ \ -x-2=-2\\\\ x=-4\ \ \ \ or\ \ \ \ \ -x=0\\\\ x=-4\ \ \ or\ \ \ \ x=0`

Answer 2

(x+2) + 16 = 14
-16] [-16
x+2 = -2
-2] [-2
x = -4

so the logical option is option 2, but you should put your numbers back into the original equation to check they're right.

when x = -4
(x+2) +16
= (-4 +2) +16
= -2 + 16
= 14 which is correct

when x = 0
(x+2) + 16
= (0+2) + 16
= 2 + 16
= 18 which is incorrect

and since we worked out x and know that none of the other numerical options are possible, I would say option 4 (no solution) is the answer.

Hope this helped.