That is absolute value.
[tex]|x|\text{ = +x or -x}[/tex][tex]\begin{gathered} |-8a\text{ - 3| > 11} \\ (-8a\text{ - 3) > 11 or -(-8a - 3) > 11} \\ (-8a\text{ - 3) > 11} \\ -8a\text{ > 11 + 3} \\ -8a\text{ > 14} \\ a\text{ < }\frac{-14}{8} \\ a\text{ < }\frac{-7}{2} \end{gathered}[/tex]or
[tex]\begin{gathered} -(-8a\text{ - 3) > 11} \\ 8a\text{ + 3 > 11} \\ 8a\text{ > 11 - 3} \\ 8a\text{ > 8} \\ a\text{ > 8/8} \\ a\text{ > 1} \end{gathered}[/tex]Therefore,
1 < a <-7/2
