Solve x - 1/3 <_ 1/2

Question

x _> 5/6

x _> 1/6

X _< 1/6

X_< 5/6

Answer 1

To solve the inequality \( x - \frac{1}{3} \leq \frac{1}{2} \), we can isolate \( x \):

1. Start with the original inequality: \[ x - \frac{1}{3} \leq \frac{1}{2} \]

2. Add \(\frac{1}{3}\) to both sides: \[ x \leq \frac{1}{2} + \frac{1}{3} \]

3. 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: \[ X \leq \frac{5}{6} \]