Let's solve the equation:

$\frac{2x}{x + 5} = \frac{-6}{x + 5} - 2$

Step 1: Eliminate the fraction by multiplying every term by $x + 5$.

Multiply both sides by $x + 5$:

$(x + 5) \cdot \frac{2x}{x + 5} = (x + 5) \cdot \left(\frac{-6}{x + 5} - 2\right)$

This simplifies to:

$2x = -6 - 2(x + 5)$

Step 2: Distribute and simplify.

Expand the right-hand side:

$2x = -6 - 2x - 10$

Combine like terms:

$2x = -2x - 16$

Step 3: Solve for $x$.

Add $2x$ to both sides:

$4x = -16$

Divide both sides by 4:

$x = -4$

Final Answer:

$x = -4$

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you solve equations involving fractions?
2. What happens when you multiply both sides of an equation by a common denominator?
3. How do you check if your solution to an equation is correct?
4. What are some special cases in solving linear equations?
5. Can you solve the equation when the variable is in the denominator?

Tip: When solving equations, always ensure you distribute correctly when multiplying terms.