Answer: x > -3/35
Step-by-step explanation:
[tex]-\frac{3}{2}\left(x-\frac{1}{3}\right)>\frac{1}{5}-5x[/tex]
[tex]=-\frac{3}{2}x+\frac{1}{2}>\frac{1}{5}-5x[/tex]
[tex]=-\frac{3}{2}x+\frac{1}{2}-\frac{1}{2}>\frac{1}{5}-5x-\frac{1}{2}[/tex]
[tex]=-\frac{3}{2}x>-5x-\frac{3}{10}[/tex]
[tex]-\frac{3}{2}x+5x>-5x-\frac{3}{10}+5x[/tex]
[tex]\frac{7}{2}x>-\frac{3}{10}[/tex]
Multiply both sides by 2:
[tex]2\cdot \frac{7}{2}x>2\left(-\frac{3}{10}\right)[/tex]
[tex]7x>-\frac{3}{5}[/tex]
Divide both sides by 7:
[tex]\frac{7x}{7}>\frac{-\frac{3}{5}}{7}[/tex] --> (-3/5 * 1/7 = -3/35)
[tex]x>-\frac{3}{35}[/tex]
