Question
What is the recommended method for representing the variable x in the equation 9x + 2 = 8x - 6 using algebra tiles?
Answers
GPT-4o mini
To represent the equation \(9x + 2 = 8x - 6\) using algebra tiles, you can follow these steps:
1. **Understand the tiles**: In algebra tiles, we typically represent:
- A positive \(x\) with a tile that is a rectangular shape.
- A negative \(x\) with a tile of the same size but a different color (usually red).
- A positive integer (constant) with a small square tile (also typically colored).
- A negative integer with a small square tile of another color.
2. **Set up the tiles for both sides of the equation**:
- For the left side \(9x + 2\):
- Use 9 positive \(x\) tiles.
- Use 2 positive constant tiles.
- For the right side \(8x - 6\):
- Use 8 positive \(x\) tiles.
- Use 6 negative constant tiles (indicated by 6 small red tiles).
3. **Visual representation**:
- Place the 9 \(x\) tiles and 2 positive tiles on one side of a balance (representing the left side of the equation).
- Place the 8 \(x\) tiles and 6 negative tiles on the other side of the balance (for the right side of the equation).
4. **Balancing the equation**:
- You can then see if both sides balance. If they do not, you can manipulate the tiles to isolate \(x\).
- To simplify, you can remove the same number of \(x\) tiles from each side. In this case, remove 8 \(x\) tiles from both sides.
- After removing 8 \(x\) tiles, you will have 1 \(x\) tile and 2 positive constant tiles on the left side, while the right side will have 6 negative constant tiles remaining.
5. **Final arrangement**:
- Now, you have:
- Left: \(x + 2\) (1 \(x\) tile and 2 positive tiles).
- Right: \(-6\) (6 negative tiles).
- To further isolate \(x\), you can remove the 2 positive tiles from both sides, leading to the left side becoming just \(x\) and the right side becoming \(-6 - 2\), which simplifies to \(-8\).
In conclusion, using algebra tiles to represent \(9x + 2 = 8x - 6\) helps visualize the balancing act of an equation. The method aids in understanding the necessary steps to isolate the variable \(x\) effectively.
1. **Understand the tiles**: In algebra tiles, we typically represent:
- A positive \(x\) with a tile that is a rectangular shape.
- A negative \(x\) with a tile of the same size but a different color (usually red).
- A positive integer (constant) with a small square tile (also typically colored).
- A negative integer with a small square tile of another color.
2. **Set up the tiles for both sides of the equation**:
- For the left side \(9x + 2\):
- Use 9 positive \(x\) tiles.
- Use 2 positive constant tiles.
- For the right side \(8x - 6\):
- Use 8 positive \(x\) tiles.
- Use 6 negative constant tiles (indicated by 6 small red tiles).
3. **Visual representation**:
- Place the 9 \(x\) tiles and 2 positive tiles on one side of a balance (representing the left side of the equation).
- Place the 8 \(x\) tiles and 6 negative tiles on the other side of the balance (for the right side of the equation).
4. **Balancing the equation**:
- You can then see if both sides balance. If they do not, you can manipulate the tiles to isolate \(x\).
- To simplify, you can remove the same number of \(x\) tiles from each side. In this case, remove 8 \(x\) tiles from both sides.
- After removing 8 \(x\) tiles, you will have 1 \(x\) tile and 2 positive constant tiles on the left side, while the right side will have 6 negative constant tiles remaining.
5. **Final arrangement**:
- Now, you have:
- Left: \(x + 2\) (1 \(x\) tile and 2 positive tiles).
- Right: \(-6\) (6 negative tiles).
- To further isolate \(x\), you can remove the 2 positive tiles from both sides, leading to the left side becoming just \(x\) and the right side becoming \(-6 - 2\), which simplifies to \(-8\).
In conclusion, using algebra tiles to represent \(9x + 2 = 8x - 6\) helps visualize the balancing act of an equation. The method aids in understanding the necessary steps to isolate the variable \(x\) effectively.