I have noticed in the past while solving inequality functions that when you want to change the inequality symbol you need to switch the $+$ or $-$ signs of the function itself.
How do I solve this equation and draw it on a number line?
$${x:|x+3|>5}$$
Algebraic solution:
If $\theta > 0$, then $$\begin{array}[t]{l}|x-a|>\theta \iff x-a>\theta \,\text{ or }\, x-a<-\theta\\ |x-a|<\theta \iff -\theta<x-a<\theta\\ |x-a|=\theta \iff x-a=\theta \,\text{ or } \,x-a=-\theta \end{array}$$
It is easy to verify the results geometrically.