Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
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
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
