Solve x−1/3≤1/2 . (1 point)

Question

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:

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