Question

Solve x−1/3≤1/2
. (1 point)
Responses

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

x≤1/6
x less-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

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:

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

This simplifies to:

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

2. Find a common denominator to add \(\frac{1}{2}\) and \(\frac{1}{3}\). The least common multiple of 2 and 3 is 6:

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

So,

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

3. Therefore, we have:

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

The solution is:

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

Thus, the correct response is:

**x ≤ 5/6.**