To solve the inequality \( x - \frac{1}{3} \leq \frac{1}{2} \), we can isolate \( x \):
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Start with the original inequality: \[ x - \frac{1}{3} \leq \frac{1}{2} \]
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Add \(\frac{1}{3}\) to both sides: \[ x \leq \frac{1}{2} + \frac{1}{3} \]
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To add \(\frac{1}{2}\) and \(\frac{1}{3}\), we need a common denominator, which is 6: \[ \frac{1}{2} = \frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6} \]
So, \[ x \leq \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \]
Thus, the solution to the inequality is: \[ x \leq \frac{5}{6} \]
So from your options, the correct answer is: \[ X \leq \frac{5}{6} \]