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Let's determine a simplified expression for the total area of Room 2 and Room 4.

### Step-by-Step Solution:

#### 1. **Determine the Area of Room 2:**
   - Room 2 has dimensions \((x + 9)\) and \(3\).
   - The area \(A_2\) of Room 2 can be calculated as:
     \[
     A_2 = (x + 9) \times 3
     \]
   - Simplifying this expression:
     \[
     A_2 = 3x + 27
     \]

#### 2. **Determine the Area of Room 4:**
   - Room 4 has dimensions \(4\) and \((x - 9)\).
   - The area \(A_4\) of Room 4 is:
     \[
     A_4 = 4 \times (x - 9)
     \]
   - Simplifying this expression:
     \[
     A_4 = 4x - 36
     \]

#### 3. **Calculate the Total Area of Room 2 and Room 4:**
   - The total area \(A_{\text{total}}\) is the sum of \(A_2\) and \(A_4\):
     \[
     A_{\text{total}} = A_2 + A_4
     \]
   - Substituting the simplified expressions for \(A_2\) and \(A_4\):
     \[
     A_{\text{total}} = (3x + 27) + (4x - 36)
     \]
   - Combining like terms:
     \[
     A_{\text{total}} = 3x + 4x + 27 - 36
     \]
     \[
     A_{\text{total}} = 7x - 9
     \]

### Final Answer:
The simplified expression representing the total area of Room 2 and Room 4 is:
\[
\boxed{7x - 9}
\]

Would you like additional details on any step, or have further questions?

Here are some related questions for further practice:
1. How would you find the area of Room 1 and Room 3?
2. What would the total area of all four rooms be?
3. How would the expression change if Room 4's dimensions were doubled?
4. How does the variable \(x\) impact the total area of Rooms 2 and 4?
5. If \(x = 5\), what is the numerical total area of Rooms 2 and 4?

**Tip:** When simplifying expressions, always combine like terms to reduce the expression to its simplest form.

Determine a simplified expression that represents the total area of Room 2 and Room 4. Be sure to show all work.

Learn how to simplify the expression for the total area of Room 2 and Room 4 in this algebraic geometry problem. This solution covers key concepts such as calculating the area of rectangles and combining like terms. Suitable for students in Grades 7-9.

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