Join the IDNLearn.com community and get your questions answered by knowledgeable individuals. Join our interactive community and access reliable, detailed answers from experienced professionals across a variety of topics.
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]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.
