To solve the inequality
\[ x - \frac{1}{3} \leq \frac{1}{2}, \]
first, we will add \(\frac{1}{3}\) to both sides:
\[ x \leq \frac{1}{2} + \frac{1}{3}. \]
To add the fractions \(\frac{1}{2}\) and \(\frac{1}{3}\), we need a common denominator. The least common multiple of 2 and 3 is 6.
Rewriting \(\frac{1}{2}\) and \(\frac{1}{3}\) with a denominator of 6:
\[ \frac{1}{2} = \frac{3}{6}, \] \[ \frac{1}{3} = \frac{2}{6}. \]
Now, we can add the two fractions:
\[ \frac{3}{6} + \frac{2}{6} = \frac{5}{6}. \]
So we have:
\[ x \leq \frac{5}{6}. \]
Thus, the solution to the inequality is:
\[ x \leq \frac{5}{6}. \]
So the correct response is:
\( x \leq \frac{5}{6} \) (x less-than-or-equal-to Start Fraction 5 over 6 End Fraction).
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