Let's solve the equation:

\[
\frac{2x}{x + 3} = \frac{-6}{x + 3} - 2
\]

### Step 1: Eliminate the fractions by multiplying every term by \( x + 3 \).

Multiply both sides by \( x + 3 \):

\[
(x + 3) \cdot \frac{2x}{x + 3} = (x + 3) \cdot \left(\frac{-6}{x + 3} - 2\right)
\]

This simplifies to:

\[
2x = -6 - 2(x + 3)
\]

### Step 2: Distribute and simplify.

Expand the right-hand side:

\[
2x = -6 - 2x - 6
\]

Combine like terms:

\[
2x = -2x - 12
\]

### Step 3: Solve for \( x \).

Add \( 2x \) to both sides:

\[
4x = -12
\]

Divide both sides by 4:

\[
x = -3
\]

### Final Answer:

\[
x = -3
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you handle equations with variables on both sides?
2. What does it mean when the variable cancels out during solving?
3. Can you explain the steps for solving linear equations?
4. How do you verify the solution to an equation?
5. What happens if you substitute \( x = -3 \) back into the original equation?

**Tip:** Always double-check your distribution when solving equations to avoid errors!

Learn how to solve the equation 2x/(x + 3) = -6/(x + 3) - 2 with a detailed step-by-step solution. This problem covers key algebraic concepts including solving equations with fractions and applying the distributive property. Suitable for students in Grades 7-9.

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