Solve inequality
||x+4|-7|<5

-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