Solve x−1/3≤1/2 . (1 point) Responses x≤5/6 x less-than-or-equal-to Start Fraction 5 over 6 End Fraction x≥5/6 x greater-than-or-equal-to Start Fraction 5 over 6 End Fraction x≥1/6 x greater-than-or-equal-to Start Fraction 1 over 6 End Fraction x≤1/6

Answer 1

To solve the inequality \( x - \frac{1}{3} \leq \frac{1}{2} \), we start by isolating \( x \).

1. Add \( \frac{1}{3} \) to both sides of the inequality:

\[ x \leq \frac{1}{2} + \frac{1}{3} \]

2. To add the fractions, we need a common denominator. The least common multiple of 2 and 3 is 6. Therefore, we convert the fractions:

\[ \frac{1}{2} = \frac{3}{6} \quad \text{and} \quad \frac{1}{3} = \frac{2}{6} \]

3. Now we can add the fractions:

\[ \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \]

Thus, we have:

\[ x \leq \frac{5}{6} \]

So the solution to the inequality \( x - \frac{1}{3} \leq \frac{1}{2} \) is:

\[ x \leq \frac{5}{6} \]

The correct response is \( x \leq \frac{5}{6} \).