https://file.aiquickdraw.com/mathbot/file/1725720281996gu1vrg24.jpg

The equation in the image appears to be:

\[
24 - \frac{(3x + 6)}{2} = -\frac{1}{2}x - 9
\]

Let's solve this step by step.

### Step 1: Simplify both sides of the equation
First, we simplify the left-hand side by distributing the subtraction.

\[
24 - \frac{3x + 6}{2} = -\frac{1}{2}x - 9
\]

### Step 2: Eliminate the fraction by multiplying everything by 2

To eliminate the fractions, multiply both sides of the equation by 2:

\[
2 \times \left( 24 - \frac{3x + 6}{2} \right) = 2 \times \left( -\frac{1}{2}x - 9 \right)
\]

Simplifying this:

\[
48 - (3x + 6) = -x - 18
\]

### Step 3: Simplify further

Now distribute on the left-hand side:

\[
48 - 3x - 6 = -x - 18
\]

Simplify the constants:

\[
42 - 3x = -x - 18
\]

### Step 4: Solve for \(x\)

Now let's move all the \(x\) terms to one side and constants to the other side:

\[
42 + 18 = -x + 3x
\]

Simplifying:

\[
60 = 2x
\]

Finally, divide by 2:

\[
x = 30
\]

### Solution:

The solution to the equation is:

\[
x = 30
\]

Would you like further clarification or details on this solution?

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Here are 5 related questions you could explore:
1. How do you solve an equation with multiple variables and fractions?
2. What are the methods to eliminate fractions in an equation?
3. How can you check if your solution to a linear equation is correct?
4. How would the equation change if there were more complex fractions?
5. Can you apply this method to solve equations with variables on both sides?

**Tip:** When solving equations with fractions, multiplying through by the least common denominator (LCD) simplifies the equation and makes it easier to solve.

Solve the equation 24 - (3x + 6) / 2 = -x / 2 - 9.

Learn how to solve the linear equation with fractions: 24 - (3x + 6) / 2 = -x / 2 - 9. This problem covers key algebraic concepts such as simplifying equations, eliminating fractions, and solving for x. Suitable for students in Grades 8-10.

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