Question

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≥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

Answer 1

To solve the inequality \( x - \frac{1}{3} \leq \frac{1}{2} \), we will isolate \( x \).

1. Start by adding \( \frac{1}{3} \) to both sides:
\[
x \leq \frac{1}{2} + \frac{1}{3}
\]

2. To add \( \frac{1}{2} \) and \( \frac{1}{3} \), we need a common denominator. The least common multiple of 2 and 3 is 6. Therefore, we convert both fractions:
\[
\frac{1}{2} = \frac{3}{6}
\]
\[
\frac{1}{3} = \frac{2}{6}
\]

3. Now we can add them together:
\[
\frac{3}{6} + \frac{2}{6} = \frac{5}{6}
\]

4. Thus, we have:
\[
x \leq \frac{5}{6}
\]

Therefore, the solution to the inequality \( x - \frac{1}{3} \leq \frac{1}{2} \) is:
\[
\boxed{x \leq \frac{5}{6}}
\]