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Solve x−1/3≤1/2

. (1 point)
Responses

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

x≥16

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:

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

  2. Find a common denominator to add the fractions. The least common denominator of 2 and 3 is 6.

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

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

  3. Now add the two fractions:

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

  4. Thus, the inequality becomes:

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

So the solution is:

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

The correct response is:

x ≤ 5/6.