Q7: What is the value of Â¦x + 7Â¦?

(1) Â¦x + 3Â¦= 14

(2) (x + 2)^2 = 169

(C) for me too

From 1
Case 1 : x+3 < 0
|x + 3|= 14

<=> -(x+3) = 14

<=> x = -17

Case 2 : x+3 > 0
|x + 3|= 14

<=> x+3 = 14

<=> x = 11

Now, let check out the values of |x+7| with these 2 values of x.

o If x = -17, then |x+7| = |-17 + 7| = 10

o If x = 11, then |x+7| = |11 + 7| = 18

INSUFF.

From 2
(x + 2)^2 = 169

<=> (x + 2)^2 - 13^2 = 0

<=> ((x+2) + 13) * ((x+2) - 13) = 0

<=> (x + 15) * (x - 11) = 0

<=> x= -15 or x = 11

Now, let check out the values of |x+7| with these 2 values of x.

o If x = -15, then |x+7| = |-15 + 7| = 8

o If x = 11, then |x+7| = |11 + 7| = 18

INSUFF.

Combined (1) with (2)
The system of solutions for x is:

o x = -17 or x = 11

and

o x= -15 or x = 11

That forces x to be equal to 11. So, |x+7| has 1 and only one value that is 18.

SUFF.