Solve x−1/3≤1/2

Question

. (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
x less-than-or-equal-to Start Fraction 5 over 6 End Fraction

Answer 1

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

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

2. Find a common denominator. The least common multiple of 2 and 3 is 6. Thus we can rewrite the fractions: \[ \frac{1}{2} = \frac{3}{6} \quad \text{and} \quad \frac{1}{3} = \frac{2}{6} \] Substituting these in gives: \[ x \leq \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \]

So the solution to the inequality is: \[ x \leq \frac{5}{6} \]

Thus, the correct response is:

• x ≤ 5/6 (x less-than-or-equal-to Start Fraction 5 over 6 End Fraction)