https://file.aiquickdraw.com/mathbot/file/1729093145217duyw9zj8.jpg

Let's break down the problem using the image of the room layout you provided:

### Objective:
We need to determine a simplified expression for the **total area** of Room 2 and Room 4. The dimensions for the rooms are given in terms of variables, and we will calculate the area for each of these rooms and then add them.

#### Room Dimensions (from the image):
- **Room 2:**
  - Width = \( x + 9 \)
  - Height = 3
  - **Area of Room 2** = \( \text{Width} \times \text{Height} = (x + 9) \times 3 \)

- **Room 4:**
  - Width = 1
  - Height = \( x - 4 \)
  - **Area of Room 4** = \( \text{Width} \times \text{Height} = 1 \times (x - 4) = x - 4 \)

### Total Area of Room 2 and Room 4:
Now, add the areas of Room 2 and Room 4:

\[
\text{Total Area} = \text{Area of Room 2} + \text{Area of Room 4}
\]

\[
\text{Total Area} = 3(x + 9) + (x - 4)
\]

### Simplify the expression:
1. Distribute the 3 in the first term:
   \[
   3(x + 9) = 3x + 27
   \]

2. Add this to the expression for Room 4's area:
   \[
   3x + 27 + x - 4
   \]

3. Combine like terms:
   \[
   (3x + x) + (27 - 4) = 4x + 23
   \]

### Final Expression:
The total area of Room 2 and Room 4 is \( 4x + 23 \).

Would you like further details on this solution or to explore related topics? Here are 5 follow-up questions:

1. What would the total area be if \( x = 5 \)?
2. How would the expression change if Room 4's width were doubled?
3. What would the combined area of all rooms be?
4. Could you express the total perimeter of Room 2 and Room 4?
5. How does factoring influence the final area expression?

**Tip:** Always distribute and combine terms carefully when simplifying expressions to avoid mistakes!

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

Learn how to calculate and simplify the total area expression for Room 2 and Room 4. This problem involves algebraic simplification, calculating the area of rectangles, and combining like terms. Suitable for students in Grades 7-9.

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