For exercise, solve the equations and inequalities. Write the solutions sets to

For exercise, solve the equations and inequalities. Write the solutions sets to the inequalities in interval notation if possible.
$\frac{1}{3}x+\frac{2}{5}>\frac{5}{6}x-1$
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Step 1
$\frac{x}{3}+\frac{2}{5}>\frac{5}{6}x-1$
Subtract $\frac{2}{5}$ from both side
$\frac{x}{3}+\frac{2}{5}-\frac{2}{5}>\frac{5}{6}x-1-\frac{2}{5}$
Step 2
$\frac{x}{3}>\frac{5}{6}x-\frac{7}{5}$
Subtract $\frac{5}{6}x$ from both side
$\frac{x}{3}-\frac{5x}{6}>\frac{5x}{6}-\frac{7}{5}-\frac{5x}{6}$
$\frac{2x-5x}{6}>\frac{-7}{5}$
$\frac{-3x}{6}>\frac{-7}{5}$
$\frac{x}{2}<\frac{7}{5}$
$x<\frac{14}{5}$
$x\in \left(-\mathrm{\infty },\frac{14}{5}\right)$