Let's simplify and solve each of the given expressions step-by-step.

**a.** \( x = \frac{1}{3} + \left(-\frac{2}{5}\right) \)

To simplify, find a common denominator for the fractions:

- Common denominator of 3 and 5 is 15.
- \(\frac{1}{3} = \frac{5}{15}\)
- \(-\frac{2}{5} = -\frac{6}{15}\)

Thus, the expression becomes:
\[ x = \frac{5}{15} - \frac{6}{15} = \frac{5 - 6}{15} = \frac{-1}{15} \]

**b.** \( \frac{x}{15} = \frac{3}{5} + \left(-\frac{2}{3}\right) \)

Simplify the right side by finding a common denominator:

- Common denominator of 5 and 3 is 15.
- \(\frac{3}{5} = \frac{9}{15}\)
- \(-\frac{2}{3} = -\frac{10}{15}\)

Thus, the equation becomes:
\[ \frac{x}{15} = \frac{9}{15} - \frac{10}{15} = \frac{-1}{15} \]

To find \( x \), multiply both sides by 15:
\[ x = -1 \]

**c.** \( \frac{11}{8} + \frac{13}{6} = \frac{85}{x} \)

First, simplify the left side by finding a common denominator:

- Common denominator of 8 and 6 is 24.
- \(\frac{11}{8} = \frac{33}{24}\)
- \(\frac{13}{6} = \frac{52}{24}\)

Add the two fractions:
\[ \frac{33}{24} + \frac{52}{24} = \frac{85}{24} \]

Set the equation \(\frac{85}{24} = \frac{85}{x}\).

Because both numerators are the same, equate the denominators:

\[ x = 24 \]

**d.** \( \frac{x}{14} = \frac{1}{7} + \left(-\frac{3}{14}\right) \)

Adjust the right side expression to a common denominator:

- Common denominator of 7 and 14 is 14.
- \(\frac{1}{7} = \frac{2}{14}\)
- \(-\frac{3}{14} = -\frac{3}{14}\)

Thus, the equation becomes:
\[ \frac{x}{14} = \frac{2}{14} - \frac{3}{14} = \frac{-1}{14} \]

To find \( x \), multiply both sides by 14:
\[ x = -1 \]

In summary:
- a. \( x = -\frac{1}{15} \)
- b. \( x = -1 \)
- c. \( x = 24 \)
- d. \( x = -1 \)