Question

How do you solve and graph `abs(x+5)<=9`?

Answer 1

With absolute values there are always two graphs, that meet at the point where the argument between the bars `=0`

Explanation:

(1) `x>=-5` no need for a sign change:
`x+5<=9->x<=9-5->x<=4`

(2) `x<-5->x+5` changes signs:
`-x-5<=9->-x<=9+5->-x<=14->x>=-14`
graph{|x+5| [-20.63, 11.41, -4.28, 11.73]}