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The equation provided is:

\[
\frac{11d + 2}{d - 8} = -\frac{3}{2}
\]

Let's solve this step by step.

### Step 1: Cross-multiply to eliminate the fractions.
\[
(11d + 2) \cdot 2 = (d - 8) \cdot (-3)
\]
Simplifying both sides:
\[
2(11d + 2) = -3(d - 8)
\]

### Step 2: Distribute on both sides.
\[
22d + 4 = -3d + 24
\]

### Step 3: Move all terms involving \(d\) to one side and constants to the other.
\[
22d + 3d = 24 - 4
\]
\[
25d = 20
\]

### Step 4: Solve for \(d\).
\[
d = \frac{20}{25} = \frac{4}{5}
\]

Thus, the solution to the equation is:
\[
d = \frac{4}{5}
\]

Would you like any further details or clarifications? 

Here are some related questions to deepen your understanding:
1. How do you verify if the solution \(d = \frac{4}{5}\) satisfies the original equation?
2. What happens if the denominator becomes zero? What values of \(d\) should be excluded from the domain?
3. How would this equation change if the right-hand side were a different fraction, such as \(\frac{3}{4}\)?
4. Can you generalize a method for solving equations of this type?
5. What are the real-world applications of such rational equations?

**Tip:** Always check for any restrictions in the domain, such as values that make the denominator zero when dealing with rational equations.

What is the solution to the given equation: (11d + 2) / (d - 8) = -3/2?

Learn how to solve the rational equation (11d + 2) / (d - 8) = -3/2 with a step-by-step solution. This problem involves algebraic techniques such as cross multiplication and the distributive property. Suitable for students in Grades 9-11.

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