Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To determine which statements correctly illustrate the addition property of equality, we'll examine each given statement.
1. If [tex]\(a = b\)[/tex], then [tex]\(a + c = b + c\)[/tex]:
- The addition property of equality states that if two expressions are equal, then adding the same value to both expressions maintains the equality. In this case, adding [tex]\(c\)[/tex] to both sides of the equation [tex]\(a = b\)[/tex] results in [tex]\(a + c = b + c\)[/tex]. This is a valid application of the addition property of equality.
2. If [tex]\(x = y\)[/tex], then [tex]\(x + 2 = y - 2\)[/tex]:
- Here, we have [tex]\(x = y\)[/tex]. To maintain equality, we must add or subtract the same value from both sides of the equation. However, adding 2 to one side and subtracting 2 from the other side, results in [tex]\(x + 2\)[/tex] and [tex]\(y - 2\)[/tex], which are not guaranteed to be equal if [tex]\(x = y\)[/tex]. This does not correctly illustrate the addition property of equality.
3. If [tex]\(w + 2 = 7\)[/tex], then [tex]\(w + 2 - 2 = 7 - 2\)[/tex]:
- Starting from the equation [tex]\(w + 2 = 7\)[/tex], subtracting the same value [tex]\(2\)[/tex] from both sides results in [tex]\(w + 2 - 2 = 7 - 2\)[/tex]. This simplifies to [tex]\(w = 5\)[/tex]. This is a correct application of the addition property of equality, demonstrating how equality is maintained when subtracting the same value from both sides.
4. If [tex]\(z - \frac{2}{5} = 9\)[/tex], then [tex]\(z - \frac{2}{5} + \frac{2}{5} = 9 - \frac{2}{5}\)[/tex]:
- From the equation [tex]\(z - \frac{2}{5} = 9\)[/tex], adding the same value [tex]\(\frac{2}{5}\)[/tex] to both sides results in [tex]\(z - \frac{2}{5} + \frac{2}{5} = 9 + \frac{2}{5}\)[/tex]. This simplifies to [tex]\(z = 9 + \frac{2}{5}\)[/tex]. This application correctly uses the addition property of equality by adding [tex]\(\frac{2}{5}\)[/tex] to both sides of the equation.
Therefore, the correct statements that illustrate the addition property of equality are:
- Statement 1: If [tex]\(a = b\)[/tex], then [tex]\(a + c = b + c\)[/tex].
- Statement 3: If [tex]\(w + 2 = 7\)[/tex], then [tex]\(w + 2 - 2 = 7 - 2\)[/tex].
- Statement 4: If [tex]\(z - \frac{2}{5} = 9\)[/tex], then [tex]\(z - \frac{2}{5} + \frac{2}{5} = 9 - \frac{2}{5}\)[/tex].
Thus, the correct statements are:
[tex]\[ \boxed{1, 3, 4} \][/tex]
1. If [tex]\(a = b\)[/tex], then [tex]\(a + c = b + c\)[/tex]:
- The addition property of equality states that if two expressions are equal, then adding the same value to both expressions maintains the equality. In this case, adding [tex]\(c\)[/tex] to both sides of the equation [tex]\(a = b\)[/tex] results in [tex]\(a + c = b + c\)[/tex]. This is a valid application of the addition property of equality.
2. If [tex]\(x = y\)[/tex], then [tex]\(x + 2 = y - 2\)[/tex]:
- Here, we have [tex]\(x = y\)[/tex]. To maintain equality, we must add or subtract the same value from both sides of the equation. However, adding 2 to one side and subtracting 2 from the other side, results in [tex]\(x + 2\)[/tex] and [tex]\(y - 2\)[/tex], which are not guaranteed to be equal if [tex]\(x = y\)[/tex]. This does not correctly illustrate the addition property of equality.
3. If [tex]\(w + 2 = 7\)[/tex], then [tex]\(w + 2 - 2 = 7 - 2\)[/tex]:
- Starting from the equation [tex]\(w + 2 = 7\)[/tex], subtracting the same value [tex]\(2\)[/tex] from both sides results in [tex]\(w + 2 - 2 = 7 - 2\)[/tex]. This simplifies to [tex]\(w = 5\)[/tex]. This is a correct application of the addition property of equality, demonstrating how equality is maintained when subtracting the same value from both sides.
4. If [tex]\(z - \frac{2}{5} = 9\)[/tex], then [tex]\(z - \frac{2}{5} + \frac{2}{5} = 9 - \frac{2}{5}\)[/tex]:
- From the equation [tex]\(z - \frac{2}{5} = 9\)[/tex], adding the same value [tex]\(\frac{2}{5}\)[/tex] to both sides results in [tex]\(z - \frac{2}{5} + \frac{2}{5} = 9 + \frac{2}{5}\)[/tex]. This simplifies to [tex]\(z = 9 + \frac{2}{5}\)[/tex]. This application correctly uses the addition property of equality by adding [tex]\(\frac{2}{5}\)[/tex] to both sides of the equation.
Therefore, the correct statements that illustrate the addition property of equality are:
- Statement 1: If [tex]\(a = b\)[/tex], then [tex]\(a + c = b + c\)[/tex].
- Statement 3: If [tex]\(w + 2 = 7\)[/tex], then [tex]\(w + 2 - 2 = 7 - 2\)[/tex].
- Statement 4: If [tex]\(z - \frac{2}{5} = 9\)[/tex], then [tex]\(z - \frac{2}{5} + \frac{2}{5} = 9 - \frac{2}{5}\)[/tex].
Thus, the correct statements are:
[tex]\[ \boxed{1, 3, 4} \][/tex]
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.