Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2 - Page 362: 55

$x=5$

$\frac{3x}{5}-x=\frac{x}{10}-\frac{5}{2}\\\frac{6x}{10}-\frac{10x}{10}=\frac{x}{15}+\frac{6}{10}-\frac{25}{10}\\\frac{-5x}{10}=\frac{-25}{10}\\-5x=-25\\x=5$ Check by plugging it in into the original equation: $\frac{3\cdot5}{5}-5=-2$. $\frac{5}{10}-\frac{5}{2}=-2$. The two sides are equal, thus it is a good solution.