How do I solve inequalities where both sides are not equal to zero, and that use absolute values and fractions? For example something like
$$\dfrac{|x-2|+3}{4-|2x+8|}\geq-5.$$
I understand how to solve inequalities where there is an absolute value, however in fraction form just confuses me.

Hint:

*

*When $4-|2x+8|>0$ the inequality is always satisfied (LHS is positive).

*When $4-|2x+8|<0$ the inequality is satisfied if and only if $|x-2|+3\leq -5(4-|2x+8|)$ (the inequality reverses when multiplying both sides by a negative number).

