Question
Use the algebra tiles tool to model the equation
5x + (–6) = 6x + 4. What is needed to model the equation? Check all that apply.
5 negative x-tiles on the left
6 positive x-tiles on the right
4positive unit tiles on the right
6 negative x-tiles on the right
6 negative unit tiles on the left
Answers
GPT-4o mini
To model the equation \(5x + (–6) = 6x + 4\) using algebra tiles, we need to represent both sides of the equation using tiles that represent the variables (x-tiles) and the constants (unit tiles).
Let's break down the equation:
- On the left side, we have \(5x\) and \(-6\).
- This can be represented with **5 positive x-tiles** (for \(5x\)) and **6 negative unit tiles** (for \(-6\)).
- On the right side, we have \(6x\) and \(4\).
- This can be represented with **6 positive x-tiles** (for \(6x\)) and **4 positive unit tiles** (for \(4\)).
Now, let's check what is needed to model the equation:
1. **5 negative x-tiles on the left** - **Not needed** (We need positive x-tiles, not negative).
2. **6 positive x-tiles on the right** - **Needed** (This represents \(6x\)).
3. **4 positive unit tiles on the right** - **Needed** (This represents the constant \(4\)).
4. **6 negative x-tiles on the right** - **Not needed** (We need positive x-tiles, not negative).
5. **6 negative unit tiles on the left** - **Needed** (This represents \(-6\), since we require negative unit tiles to model \(-6\)).
In summary, the correct selections for modeling the equation are:
- **6 positive x-tiles on the right**
- **4 positive unit tiles on the right**
- **6 negative unit tiles on the left**
Let's break down the equation:
- On the left side, we have \(5x\) and \(-6\).
- This can be represented with **5 positive x-tiles** (for \(5x\)) and **6 negative unit tiles** (for \(-6\)).
- On the right side, we have \(6x\) and \(4\).
- This can be represented with **6 positive x-tiles** (for \(6x\)) and **4 positive unit tiles** (for \(4\)).
Now, let's check what is needed to model the equation:
1. **5 negative x-tiles on the left** - **Not needed** (We need positive x-tiles, not negative).
2. **6 positive x-tiles on the right** - **Needed** (This represents \(6x\)).
3. **4 positive unit tiles on the right** - **Needed** (This represents the constant \(4\)).
4. **6 negative x-tiles on the right** - **Not needed** (We need positive x-tiles, not negative).
5. **6 negative unit tiles on the left** - **Needed** (This represents \(-6\), since we require negative unit tiles to model \(-6\)).
In summary, the correct selections for modeling the equation are:
- **6 positive x-tiles on the right**
- **4 positive unit tiles on the right**
- **6 negative unit tiles on the left**