TITLE: what is the process to solving this absolute value inequality: $4-\left|\frac{5y}{3}+4\right| > \frac25$?
QUESTION [5 upvotes]: I keep trying to solve it but I seem to be making an error somewhere: 
 $$4-\left|\frac{5y}{3}+4\right| > \frac25$$

REPLY [4 votes]: $4-\left|\frac{5y}{3}+4\right| > \frac25$ can be rewritten as $-\left|\frac{5y}{3}+4\right| > \frac{-18}{5}$ or $\left|\frac{5y}{3}+4\right| < \frac{18}{5}$. From here, represent the expression as $\frac{-18}{5} < \frac{5y}{3}+4\ < \frac{18}{5}$ and proceed to solve it using arithmetic.