Example

Solve for $r$: $\quad -5|r-4|+12 > -28$

Solution

First, we isolate the absolute value expression.

Notice that the inequality reversed when we divided by $-5$.

This inequality tells us that the number between the absolute value bars is less than $8$ units from $0$. In other words,

This compound inequality is an "AND" inequality, and it can be solved by adding $4$ all the way across the inequalities.

In interval notation, this solution is $(-4,12)$, and the corresponding number line is