Problem Solving

hi guys,
This problem is from kaplan and I wasn't clear with their explanation.

1) Which of the following describess all values of x that are solutions to the inequality |x+2| > 6?

a) x>4
b) x>8
c) x < -8 or x>4
d) x<4 or x > 8
e) -8<x<4

Thanks in advance,
Karthik

Hello,

The Abosolut value rule:

lxl>a -------> x>a and x<-a
lxl<a -------> -a<x<a

In this case,

lx+2l>6 ------> x>4
lx+2l<-6 ------> x<-8

Hence C...

answer should be C

try to imagine absolute values on number line

--------------------------------------------------------------->
......................-6......................0.........................+6
..............x+2<-6.................................................x>6
substract 2 from x, -6 and 6 you'll get
......x<-8....................................................x>4

another way

|x+2|>6
-6>x+2>6
substract 2
-8>x>4

Answer C