Question

Solve x−1/3≤1/2 . (1 point)
Responses

x≥5/6
x greater-than-or-equal-to Start Fraction 5 over 6 End Fraction

x≤5/6
x less-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 can follow these steps:

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

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

2. **Find a common denominator**: The common denominator for 2 and 3 is 6.

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

3. **Add the fractions**:

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

4. **Write the final result**:

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

The solution to the inequality is:

**\( x \leq \frac{5}{6} \)**, which corresponds to the second response option provided:

\( x \text{ less-than-or-equal-to } \frac{5}{6} \).