To solve the equation \(\frac{1}{2}x + \frac{3}{5}x = -\frac{2}{3}\), follow these steps:

1. **Combine the terms involving \(x\):**

\[
\frac{1}{2}x + \frac{3}{5}x
\]

To combine these fractions, find a common denominator. The least common multiple of 2 and 5 is 10.

\[
\frac{1}{2}x = \frac{5}{10}x \quad \text{and} \quad \frac{3}{5}x = \frac{6}{10}x
\]

So,

\[
\frac{5}{10}x + \frac{6}{10}x = \frac{11}{10}x
\]

The equation now becomes:

\[
\frac{11}{10}x = -\frac{2}{3}
\]

2. **Solve for \(x\):**

To isolate \(x\), multiply both sides of the equation by the reciprocal of \(\frac{11}{10}\), which is \(\frac{10}{11}\):

\[
x = -\frac{2}{3} \times \frac{10}{11}
\]

3. **Simplify the right-hand side:**

\[
x = -\frac{2 \times 10}{3 \times 11} = -\frac{20}{33}
\]

So, the solution to the equation \(\frac{1}{2}x + \frac{3}{5}x = -\frac{2}{3}\) is:

\[
x = -\frac{20}{33}
\]