Solve x−1/3≤1/2

. (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

1 answer

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

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

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

  1. To add \( \frac{1}{2} \) and \( \frac{1}{3} \), you first need a common denominator. The least common multiple of 2 and 3 is 6. Convert both fractions:

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

  1. Now, add the fractions:

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

  1. Thus, the inequality becomes:

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

The correct response is:

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