#### Answer

$\frac{1}{6}$ is indeed a solution of this equation.

#### Work Step by Step

Let's plug in $\frac{1}{6}$ for $x$ to see if the equation holds true. If it does, then $\frac{1}{6}$ is a solution of the equation:
$$-\frac{1}{2} = \frac{1}{6} - \frac{2}{3}$$
To work with fractions, we need to make sure they have the same denominator. We must find the lowest common denominator for all three fractions.
$6$ seems to be the common denominator for all three fractions. We need to multiply each fraction by the lowest common denominator to get rid of the fractions:
$$6(-\frac{1}{2}) = 6(\frac{1}{6}) - 6(\frac{2}{3})$$
Cancel out common factors:
$$-3 = 1 - 4$$
Subtract:
$$-3 = -3$$
Because the two sides of the equation equal one another, $\frac{1}{6}$ is indeed a solution of this equation.