To solve the equation:

\[
-\frac{3}{2} - \frac{3}{2}x = -\frac{3}{5}
\]

### Step 1: Eliminate the fraction on the left side
Add \(\frac{3}{2}\) to both sides to isolate the term with \(x\):

\[
-\frac{3}{2}x = -\frac{3}{5} + \frac{3}{2}
\]

### Step 2: Find a common denominator
The common denominator between 5 and 2 is 10. Rewrite both fractions with a denominator of 10:

\[
-\frac{3}{5} = -\frac{6}{10}, \quad \frac{3}{2} = \frac{15}{10}
\]

Now, add the fractions:

\[
-\frac{3}{5} + \frac{3}{2} = -\frac{6}{10} + \frac{15}{10} = \frac{9}{10}
\]

So, the equation becomes:

\[
-\frac{3}{2}x = \frac{9}{10}
\]

### Step 3: Solve for \(x\)
Divide both sides of the equation by \(-\frac{3}{2}\), or equivalently, multiply both sides by \(-\frac{2}{3}\):

\[
x = \frac{9}{10} \times \left(-\frac{2}{3}\right) = -\frac{18}{30}
\]

Simplify the fraction:

\[
x = -\frac{3}{5}
\]

### Final Answer:
\[
x = -\frac{3}{5}
\]

Would you like any further details or clarifications?

Here are five related questions:
1. How do you solve linear equations with variables on both sides?
2. What are some methods for solving equations with fractions?
3. How can we eliminate fractions from an equation?
4. Why is finding a common denominator important when adding fractions?
5. How do you simplify a fraction after multiplying?

**Tip:** When solving equations with fractions, finding a common denominator can help simplify the process.

Explore the step-by-step solution for solving the linear equation with fractions: -3/2 - 3/2x = -3/5. Understand key algebraic concepts like adding fractions and isolating variables, suitable for Grades 6-8.

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