Solve x−1/3≤1/2

Question

. (1 point)
Responses

x≥16
x greater-than-or-equal-to Start Fraction 1 over 6 End Fraction

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

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

x≥56

Answer 1

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

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

2. Find a common denominator (which is 6) to add the fractions: \[ \frac{1}{2} = \frac{3}{6} \quad \text{and} \quad \frac{1}{3} = \frac{2}{6} \] Thus, \[ \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \]

3. Now the inequality becomes: \[ x \leq \frac{5}{6} \]

Therefore, the solution is: \[ x \leq \frac{5}{6} \]

Among the provided responses, the correct one is: x less-than-or-equal-to Start Fraction 5 over 6 End Fraction.