Solve the inequality for \( x \) \[ x+\frac{2}{5}<\frac{1}{6} \] Simplify your answer as muc D.

To solve the inequality \( x + \frac{2}{5} < \frac{1}{6} \), start by isolating \( x \). 1. Subtract \(\frac{2}{5}\) from both sides: \[ x < \frac{1}{6} - \frac{2}{5} \] 2. To perform the subtraction, we need a common denominator. The least common multiple of 6 and 5 is 30. Convert \(\frac{1}{6}\) and \(\frac{2}{5}\) to have a denominator of 30: \[ \frac{1}{6} = \frac{5}{30} \quad \text{and} \quad \frac{2}{5} = \frac{12}{30} \] 3. Now, substitute these values back into the inequality: \[ x < \frac{5}{30} - \frac{12}{30} \] 4. Perform the subtraction: \[ x < \frac{5 - 12}{30} = \frac{-7}{30} \] Thus, the solution to the inequality is: \[ x < \frac{-7}{30} \]