Answer :
To model the equation [tex]\(5x + (-6) = 6x + 4\)[/tex] using algebra tiles, we need to arrange the appropriate number and type of tiles on both sides of the equation.
Here's how we can do it step-by-step:
1. Identify the terms on both sides of the equation:
- On the left side: [tex]\(5x\)[/tex] and [tex]\(-6\)[/tex]
- On the right side: [tex]\(6x\)[/tex] and [tex]\(4\)[/tex]
2. Model the left side of the equation:
- 5 negative [tex]\(x\)[/tex] tiles on the left: We need 5 negative [tex]\(x\)[/tex] tiles to represent [tex]\(5x\)[/tex] on the left side. Each tile corresponds to [tex]\(-x\)[/tex], so to have 5 negative [tex]\(x\)[/tex] tiles, we write this as 5 positive [tex]\(x\)[/tex] tiles visually but conceptually as [tex]\(5x\)[/tex].
- 6 negative unit tiles on the left: We need 6 negative unit tiles to represent [tex]\(-6\)[/tex].
3. Model the right side of the equation:
- 6 positive [tex]\(x\)[/tex] tiles on the right: We need 6 positive [tex]\(x\)[/tex] tiles to represent [tex]\(6x\)[/tex].
- 4 positive unit tiles on the right: We need 4 positive unit tiles to represent [tex]\(4\)[/tex].
4. Check which tiles we need:
- 5 negative [tex]\(x\)[/tex] tiles on the left: Yes, needed to represent [tex]\(5x\)[/tex].
- 6 positive [tex]\(x\)[/tex] tiles on the right: Yes, needed to represent [tex]\(6x\)[/tex].
- 4 positive unit tiles on the right: Yes, needed to represent [tex]\(4\)[/tex].
- 6 negative [tex]\(x\)[/tex] tiles on the right: No, not needed, it would incorrectly add [tex]\(-6x\)[/tex] to the right side.
- 6 negative unit tiles on the left: No, they are on the right side and we only need 4 of them.
So, we conclude that the needed items to model this equation and make the board sum to 0 are:
- 5 negative [tex]\(x\)[/tex] tiles on the left
- 6 positive [tex]\(x\)[/tex] tiles on the right
- 4 positive unit tiles on the right
Thus, the correct items are:
- 5 negative [tex]\(x\)[/tex] tiles on the left
- 6 positive [tex]\(x\)[/tex] tiles on the right
- 4 positive unit tiles on the right
Items that are not needed:
- 6 negative [tex]\(x\)[/tex] tiles on the right
- 6 negative unit tiles on the left
Therefore, the true selections are:
- 5 negative [tex]\(x\)[/tex] tiles on the left
- 6 positive [tex]\(x\)[/tex] tiles on the right
- 4 positive unit tiles on the right
Here's how we can do it step-by-step:
1. Identify the terms on both sides of the equation:
- On the left side: [tex]\(5x\)[/tex] and [tex]\(-6\)[/tex]
- On the right side: [tex]\(6x\)[/tex] and [tex]\(4\)[/tex]
2. Model the left side of the equation:
- 5 negative [tex]\(x\)[/tex] tiles on the left: We need 5 negative [tex]\(x\)[/tex] tiles to represent [tex]\(5x\)[/tex] on the left side. Each tile corresponds to [tex]\(-x\)[/tex], so to have 5 negative [tex]\(x\)[/tex] tiles, we write this as 5 positive [tex]\(x\)[/tex] tiles visually but conceptually as [tex]\(5x\)[/tex].
- 6 negative unit tiles on the left: We need 6 negative unit tiles to represent [tex]\(-6\)[/tex].
3. Model the right side of the equation:
- 6 positive [tex]\(x\)[/tex] tiles on the right: We need 6 positive [tex]\(x\)[/tex] tiles to represent [tex]\(6x\)[/tex].
- 4 positive unit tiles on the right: We need 4 positive unit tiles to represent [tex]\(4\)[/tex].
4. Check which tiles we need:
- 5 negative [tex]\(x\)[/tex] tiles on the left: Yes, needed to represent [tex]\(5x\)[/tex].
- 6 positive [tex]\(x\)[/tex] tiles on the right: Yes, needed to represent [tex]\(6x\)[/tex].
- 4 positive unit tiles on the right: Yes, needed to represent [tex]\(4\)[/tex].
- 6 negative [tex]\(x\)[/tex] tiles on the right: No, not needed, it would incorrectly add [tex]\(-6x\)[/tex] to the right side.
- 6 negative unit tiles on the left: No, they are on the right side and we only need 4 of them.
So, we conclude that the needed items to model this equation and make the board sum to 0 are:
- 5 negative [tex]\(x\)[/tex] tiles on the left
- 6 positive [tex]\(x\)[/tex] tiles on the right
- 4 positive unit tiles on the right
Thus, the correct items are:
- 5 negative [tex]\(x\)[/tex] tiles on the left
- 6 positive [tex]\(x\)[/tex] tiles on the right
- 4 positive unit tiles on the right
Items that are not needed:
- 6 negative [tex]\(x\)[/tex] tiles on the right
- 6 negative unit tiles on the left
Therefore, the true selections are:
- 5 negative [tex]\(x\)[/tex] tiles on the left
- 6 positive [tex]\(x\)[/tex] tiles on the right
- 4 positive unit tiles on the right
