[tex]\bold{Answer}[/tex]
[tex]\boxed{\bold{\frac{5x-3}{2x-1}<0}}[/tex]
[tex]\bold{Explanation}[/tex]
- [tex]\bold{Solve: \ \frac{1}{2x-1}>5}[/tex]
[tex]\bold{---------------------}[/tex]
- [tex]\bold{Subtract \ 5 \ From \ Both \ Sides}[/tex]
[tex]\bold{\frac{1}{2x-1}-5>5-5}[/tex]
- [tex]\bold{Simplify}[/tex]
[tex]\bold{\frac{1}{2x-1}-5>0}[/tex]
- [tex]\bold{Simplify \ \frac{1}{2x-1}-5: \ \frac{-10x+6}{2x-1}>0}[/tex]
[tex]\bold{\frac{-10x+6}{2x-1}>0}[/tex]
- [tex]\bold{Factor \ \frac{-10x+6}{2x-1}: \ \frac{-2\left(5x-3\right)}{2x-1}>0}[/tex]
[tex]\bold{\frac{-2\left(5x-3\right)}{2x-1}>0}[/tex]
- [tex]\bold{Multiply \ Both \ Sides \ By \ -1 \ (Reverse \ Inequality)}[/tex]
[tex]\bold{\frac{\left(-2\left(5x-3\right)\right)\left(-1\right)}{2x-1}<0\cdot \left(-1\right)}[/tex]
- [tex]\bold{Simplify}[/tex]
[tex]\bold{\frac{2\left(5x-3\right)}{2x-1}<0}[/tex]
- [tex]\bold{Divide \ Both \ Sides \ By \ 2}[/tex]
[tex]\bold{\frac{\frac{2\left(5x-3\right)}{2x-1}}{2}<\frac{0}{2}}[/tex]
- [tex]\bold{Simplify}[/tex]
[tex]\bold{\frac{5x-3}{2x-1}<0}[/tex]
[tex]\boxed{\bold{Eclipsed}}[/tex]
