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.
