Chapter 1 - Solving Linear Equations - 1.3 - Solving Equations with Variables on Both Sides - Monitoring Progress - Page 21: 5

$\text{no solution}$

$$\begin{align*} 5m&=\frac{5}{6}\left(6m-10\right)&\text{Combine like terms.}\\ 5m&=\frac{5}{6}(6m)-\frac{5}{6}(10) &\text{Apply the Distributive Property.}\\ 5m&=5m-\frac{25}{3} &\text{Simplify.}\\ 5m-5m&=5m-\frac{25}{3}-5m &\text{Subtract $5m$ from each side.}\\ 0&=-\frac{25}{3} &\text{Simplify.}\\ \end{align*}$$ The last line is a false statement. so the equation has no solution.