Solve x−1/3≤1/2 . (1 point)

Question

Responses

x≥1/6
x greater-than-or-equal-to Start Fraction 1 over 6 End Fraction

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

Answer 1

To solve the inequality \( x - \frac{1}{3} \leq \frac{1}{2} \), follow these steps:

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

2. Find a common denominator for the fractions on the right side. The common denominator for 2 and 3 is 6. Thus: \[ \frac{1}{2} = \frac{3}{6} \quad \text{and} \quad \frac{1}{3} = \frac{2}{6} \]

3. Add the fractions: \[ \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \]

4. So the inequality becomes: \[ x \leq \frac{5}{6} \]

Thus, the final solution is \( x \leq \frac{5}{6} \).

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