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.

Add +5 to both sides and you got 0 on one side.
Now add the two terms you got on the left (you may want to search about the least common multiple)
Now the inequality is asking you for what values of x your fraction is greater than or equal to 0.
The answer is: for every value of x that makes numerator and denominator either botth positive or both negative.
