Question

What is the solution set for the inequality |-3-5x|-8<-2

Answer 1

The hard way:

$\left| -3-5x \right| -8$

$\\ \\ 9+15x+15x+25{ x }^{ 2 }$

$\\ \\ 25{ x }^{ 2 }+30x-27=0\\ \\ 25{ x }^{ 2 }+30x=27\\ \\ { x }^{ 2 }+\frac { 30 }{ 25 } x=\frac { 27 }{ 25 } \\ \\ { x }^{ 2 }+\frac { 6 }{ 5 } x=\frac { 27 }{ 25 } \\ \\ { \left( x+\frac { 3 }{ 5 } \right) }^{ 2 }-{ \left( \frac { 3 }{ 5 } \right) }^{ 2 }=\frac { 27 }{ 25 }$

$\\ \\ { \left( x+\frac { 3 }{ 5 } \right) }^{ 2 }=\frac { 36 }{ 25 } \\ \\ x+\frac { 3 }{ 5 } =\pm \frac { 6 }{ 5 } \\ \\ x=-\frac { 3 }{ 5 } \pm \frac { 6 }{ 5 }$

$Therefore:\\ \\ x=\frac { 3 }{ 5 } \quad and\quad x=-\frac { 9 }{ 5 } \quad when\quad f\left( x \right) =0\\ \\ Now:\\ \\ f\left( x \right)$

When:

-9/5<x<3/5

Answer 2

$|-3-5x|-8$