Introductory Algebra for College Students (7th Edition)

$$x = -\frac{5}{3}$$
First, multiply by the least common denominator to get rid of the fractions. The least common denominator, in this case, is $30$: $$30(\frac{x}{5} - \frac{1}{3}) = 30(\frac{x}{10} - \frac{1}{2})$$ Divide out common factors to get rid of the fractions: $$6x - 10 = 3x - 15$$ Subtract $3x$ from both sides to get the variable on one side of the equation: $$6x - 10 - 3x = -15$$ Combine variable terms: $$3x - 10 = -15$$ Add $10$ to both sides of the equation to get the constants on one side of the equation: $$3x = -5$$ Divide both sides by $3$ to solve for $x$: $$x = -\frac{5}{3}$$