Write as one inequality with an absolute value x Solutionx

Write as one inequality with an absolute value. x

Solution

x<-5 or 8<x

we see that given region is not between -5 and 8 so formula will be of type
|x+a|>b
or b<x+a<-b
or b<x+a , x+a<-b
or b-a<x , x<-b-a
or x<-b-a , b-a<x
now compare it with given values we get:
-b-a=-5 and b-a=8
now we just need to sovle above equations for a and b
adding both gives
-2a=3
a=-3/2
now plug a=-3/2 into
b-a=8
b-(-3/2)=8
b=8-3/2
b=13/2

now plug values of a and b into |x+a|>b
answer will be |x-3/2|>13/2