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18. Name the property of equality that justifies the following statement:

If [tex]p = q[/tex], then [tex]p - r = q - r[/tex].

A. Multiplication Property
B. Reflexive Property
C. Symmetric Property
D. Subtraction Property

Sagot :

GinnyAnswer
Certainly! Let's analyze the statement provided:

If [tex]\( p = q \)[/tex], then [tex]\( p - r = q - r \)[/tex].

To determine the property of equality that justifies this statement, we need to understand each property provided as options.

1. Multiplication Property: This property states that if [tex]\( p = q \)[/tex], then [tex]\( p \times r = q \times r \)[/tex]. Clearly, this involves multiplication, not subtraction.

2. Reflexive Property: This property states that any number is equal to itself, i.e., [tex]\( p = p \)[/tex]. It doesn't relate to the subtraction between two sides of an equation.

3. Symmetric Property: This property states that if [tex]\( p = q \)[/tex], then [tex]\( q = p \)[/tex]. It involves switching the sides of the equation, not using subtraction.

4. Subtraction Property: This property states that if [tex]\( p = q \)[/tex], then subtracting the same amount [tex]\( r \)[/tex] from both [tex]\( p \)[/tex] and [tex]\( q \)[/tex] results in [tex]\( p - r = q - r \)[/tex]. This exactly matches the given statement.

Therefore, the property of equality that justifies the statement "If [tex]\( p = q \)[/tex], then [tex]\( p - r = q - r \)[/tex]" is the Subtraction Property.
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