solve the inequality
$\displaystyle \left| 5x+4\right| >6$
$\displaystyle |5x+4| = \left\{\begin{array}{lcr}5x+4 &if& x\geq -\frac45\\ -(5x+4)&if &x < -\frac45\end{array}\right.$
That means you have 2 inequalities:
$\displaystyle \begin{array}{lcr}5x+4>6 &if& x\geq -\frac45\\ -(5x+4)>6&if &x < -\frac45\end{array}$
$\displaystyle \begin{array}{lcr}x> \frac25 &if& x\geq -\frac45\\ x<-2&if &x < -\frac45\end{array}$
The solution of this inequality is: $\displaystyle x < -2~\vee~x > \frac25$