1.
[tex]|-8x-3|>1[/tex]we separate the inequality into two parts to solve the absolute value
[tex]\begin{gathered} -8x-3>1 \\ \& \\ -8x-3<-1 \end{gathered}[/tex]first part
[tex]\begin{gathered} -8x-3>1 \\ -3-1>8x \\ -\frac{4}{8}>x \\ \\ x<-\frac{1}{2} \end{gathered}[/tex]second part
[tex]\begin{gathered} -8x-3<-1 \\ -3+1<8x \\ -\frac{2}{8}-\frac{1}{4} \end{gathered}[/tex]graph
where the yellow lines are the first part, red the second part and the solution of the inequality is the union of these two
[tex]\begin{gathered} x<-\frac{1}{2} \\ or \\ x>-\frac{1}{4} \end{gathered}[/tex]2.
[tex]\begin{gathered} |x+5|-6<-5 \\ |x+5|<1 \end{gathered}[/tex]we separate the inequality into two parts to solve the absolute value
[tex]\begin{gathered} x+5<1 \\ \& \\ x+5>-1 \end{gathered}[/tex]first part
[tex]\begin{gathered} x+5<1 \\ x<1-5 \\ x<-4 \end{gathered}[/tex]second part
[tex]\begin{gathered} x+5>-1 \\ x>-1-5 \\ x>-6 \end{gathered}[/tex]graph
where the first part is yellow, the second part is red and the solution of the inequality is green
[tex]-4>x>-6[/tex]
