Let's solve the equation step by step:

Given equation:
\[
11 + \frac{1}{3}(9w - 12) = -5(5 + w)
\]

### Step 1: Simplify both sides
Start by distributing the \(\frac{1}{3}\) on the left side and \(-5\) on the right side.

\[
11 + \frac{1}{3} \times 9w - \frac{1}{3} \times 12 = -5 \times 5 - 5 \times w
\]
\[
11 + 3w - 4 = -25 - 5w
\]

### Step 2: Combine like terms
Simplify both sides:

\[
(11 - 4) + 3w = -25 - 5w
\]
\[
7 + 3w = -25 - 5w
\]

### Step 3: Move the terms involving \(w\) to one side and the constant terms to the other side
Add \(5w\) to both sides and subtract 7 from both sides:

\[
3w + 5w = -25 - 7
\]
\[
8w = -32
\]

### Step 4: Solve for \(w\)
Divide both sides by 8:

\[
w = \frac{-32}{8}
\]
\[
w = -4
\]

### Final answer:
\[
w = -4
\]

Would you like further clarification or more details? 

Here are five related questions to expand this topic:
1. How would the solution change if the constants were different in the original equation?
2. Can you solve an equation like this with fractions on both sides?
3. How do you handle distributive property with negative signs in more complex equations?
4. What happens if there are variables on both sides of the equation and fractions as well?
5. How does solving for a variable in this equation change if there are additional variables?

**Tip:** Always simplify fractions and distribute terms before moving terms across the equal sign in equations!

This page provides a detailed step-by-step solution for solving the linear equation 11 + 1/3(9w - 12) = -5(5 + w). Learn key algebra concepts like the distributive property, combining like terms, and solving for a variable. Suitable for students in Grades 8-10.

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