first off, let's bear in mind that, an absolute value expression is in effect a piecewise one, since it has a ±versions.
[tex]\bf |4k-8|+8<11\\\\\\ |4k-8|<3 \begin{cases} +(4k-8)<3\implies 4k<11\implies k<\cfrac{11}{4}\\[-0.5em] \hrulefill\\ -(4k-8)<3\implies 4k-8\stackrel{\stackrel{notice}{\downarrow }}{>}-3\\[0.8em] 4k>5\implies k>\cfrac{5}{4}\\[-0.5em] \hrulefill\\ ~\hfill \frac{5}{4}<k<\frac{11}{4}~\hfill \end{cases}[/tex]
