https://file.aiquickdraw.com/mathbot/file/1729550684365gpofjbas.jpg

The equation given in the image is:

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

Let's solve for \( w \).

### Step 1: Simplify both sides of the equation.

First, simplify the left-hand side (LHS):

\[
\frac{1}{3}(9w - 12) = \frac{1}{3} \times 9w - \frac{1}{3} \times 12 = 3w - 4
\]

So, the left-hand side becomes:

\[
11 + 3w - 4 = 7 + 3w
\]

Now, simplify the right-hand side (RHS):

\[
-5(5 + w) = -25 - 5w
\]

### Step 2: Set up the simplified equation.

Now we have:

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

### Step 3: Combine like terms.

To eliminate \( w \) from one side, add \( 5w \) to both sides:

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

This simplifies to:

\[
7 + 8w = -25
\]

### Step 4: Isolate \( w \).

Subtract 7 from both sides:

\[
8w = -25 - 7
\]

\[
8w = -32
\]

### Step 5: Solve for \( w \).

Divide both sides by 8:

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

Thus, the value of \( w \) that makes the equation true is \( w = -4 \).

Would you like further details or clarifications on any of the steps?

Here are some related questions to deepen your understanding:
1. How would the solution change if the constant term on the left-hand side were different?
2. Can you solve similar equations with different fractions?
3. How do you deal with variables on both sides of the equation?
4. What happens if there were more variables in the equation?
5. How can this equation be checked for correctness after solving?

**Tip:** Always simplify both sides of an equation as much as possible before solving for the variable to make the process easier.

What value of w makes the equation 11 + (1/3)(9w - 12) = -5(5 + w) true?

Find the value of w that satisfies the equation 11 + (1/3)(9w - 12) = -5(5 + w). This solution involves applying the distributive property, combining like terms, and isolating the variable. Detailed step-by-step calculations are provided for better understanding.

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