Answer:
-16<x<-6 OR -2<x<8
Step-by-step explanation:
||x+4|-7|<5 implies the following:
|x+4|-7<5 and |x+4|-7>-5
Now adding 7 on both sides of each inequality gives:
|x+4|<12 and |x+4|>2
The first one implies x+4<12 and x+4>-12.
The second one impliee x+4>2 or x+4<-2.
Now let's subtract 4 on both sides for all of the inequalities.
The first implication gives: x<8 and x>-16.
This means everything between-16 and 8 is a solution.
The second implication gives x>-2 or x<-6.
This means everything greater than less than -6 or everything greater than -2 is a solution.
Taking the intersection of these implications gives:
Only numbers between -2 and 8 or only numbers between-16 and -6 are solutions.
Inequality notation:
-16<x<-6 OR -2<x<8
