Solve x−1/3≤1/2

Question

. (1 point)
Responses

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

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

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

x≤56

Answer 1

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

1. Add \( \frac{1}{3} \) to both sides of the inequality:

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

2. To add the fractions, we need a common denominator. The least common multiple of 2 and 3 is 6. Convert the fractions:

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

3. Now, add them together:

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

4. Thus, the inequality becomes:

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

So the solution is:

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