Question

explain the difference between solving |x+3|>4 and |x+3|<4.

Answer 1

−4>|x+3|>4
-7>x>-1

\[-4< |x+3|<4.\]
-7<x<1

I solved each equation you listed. What do you think is the difference?

Answer 2

\[\left| x \right|>a means x<-a and x>a\] or does not lie between -a and a.
\[\left| x \right|<a means -a<x<a\] or lies between -a and a.