Answer
$$x = -\frac{5}{3}$$
Work Step by Step
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 $x$:
$$x = -\frac{5}{3}$$
