Answer :
Certainly! Let's go through the reasoning step-by-step to determine which property is being demonstrated in the given example:
1. Understand the Statement:
- We are given that [tex]\( x = 6 \)[/tex] and [tex]\( y = 6 \)[/tex].
- We are asked about the property shown by claiming [tex]\( x + 9 = y + 9 \)[/tex].
2. Analyze the Information:
- Since [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are both equal to 6, they are already established as equal: [tex]\( x = y \)[/tex].
3. Apply the Property:
- The statement [tex]\( x + 9 = y + 9 \)[/tex] is true because we are adding the same number (9) to both sides of the equation [tex]\( x = y \)[/tex].
- This demonstrates a fundamental property of equality: if two things are equal, and you do the same operation to both of them, they remain equal.
4. Identify the Property:
- The property that allows you to add the same number to both sides of an equation and maintain equality is known as the Equality Property.
- This property states that if [tex]\( a = b \)[/tex], then [tex]\( a + c = b + c \)[/tex].
Therefore, the property being illustrated in this example is the Equality Property.
1. Understand the Statement:
- We are given that [tex]\( x = 6 \)[/tex] and [tex]\( y = 6 \)[/tex].
- We are asked about the property shown by claiming [tex]\( x + 9 = y + 9 \)[/tex].
2. Analyze the Information:
- Since [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are both equal to 6, they are already established as equal: [tex]\( x = y \)[/tex].
3. Apply the Property:
- The statement [tex]\( x + 9 = y + 9 \)[/tex] is true because we are adding the same number (9) to both sides of the equation [tex]\( x = y \)[/tex].
- This demonstrates a fundamental property of equality: if two things are equal, and you do the same operation to both of them, they remain equal.
4. Identify the Property:
- The property that allows you to add the same number to both sides of an equation and maintain equality is known as the Equality Property.
- This property states that if [tex]\( a = b \)[/tex], then [tex]\( a + c = b + c \)[/tex].
Therefore, the property being illustrated in this example is the Equality Property.
