Given:
The inequality is,
[tex]\lvert x+11\rvert<17[/tex]Solve the inequality,
[tex]\begin{gathered} \lvert x+11\rvert<17 \\ Apply\text{ absolute rule, }\mathrm{If}\: |x|\: <\: a,for\: a>0\: \mathrm{then}\: -a\: <\: x\: <\: a \\ -17-17\text{ and x+11<17} \\ x>-17-11\text{ and x<17-11} \\ x>-28\text{ and x< }6 \end{gathered}[/tex]The solution of given inequality is,
[tex]x<6,x>-28[/tex]Answer: Option D.