Question

Solve x−1/3≤1/2
. (1 point)
Responses

x≤56
x less-than-or-equal-to Start Fraction 5 over 6 End Fraction

x≤16
x less-than-or-equal-to Start Fraction 1 over 6 End Fraction

x≥56
x greater-than-or-equal-to Start Fraction 5 over 6 End Fraction

x≥16

Answer 1

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

1. Add \( \frac{1}{3} \) 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. So we can convert the fractions:

\[
\frac{1}{2} = \frac{3}{6} \quad \text{and} \quad \frac{1}{3} = \frac{2}{6}
\]
So now we add them:

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

Thus, the solution to the inequality is:

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

The correct response is: **x less-than-or-equal-to Start Fraction 5 over 6 End Fraction**.