To solve the problem, let's consider the properties of equality, which are fundamental rules governing algebraic operations that preserve equality. Specifically, the properties include:
1. Addition Property of Equality: If [tex]\( x = y \)[/tex], then [tex]\( x + a = y + a \)[/tex] for any number [tex]\( a \)[/tex]. This allows us to add the same quantity to both sides of an equation without changing the equality.
2. Subtraction Property of Equality: If [tex]\( x = y \)[/tex], then [tex]\( x - a = y - a \)[/tex] for any number [tex]\( a \)[/tex]. This allows us to subtract the same quantity from both sides of an equation without changing the equality.
3. Multiplication Property of Equality: If [tex]\( x = y \)[/tex], then [tex]\( x \cdot z = y \cdot z \)[/tex] for any number [tex]\( z \)[/tex]. This means multiplying both sides of an equation by the same non-zero quantity does not affect the equality.
4. Division Property of Equality: If [tex]\( x = y \)[/tex], then [tex]\( \frac{x}{z} = \frac{y}{z} \)[/tex] for any non-zero number [tex]\( z \)[/tex]. This allows dividing both sides of an equation by the same non-zero quantity without affecting the equality.
Given:
[tex]\[ x = y \][/tex]
By examining the expression [tex]\( x \cdot z = y \cdot z \)[/tex], we observe that this property involves multiplying both sides of an equation by the same number [tex]\( z \)[/tex]. This is described by the Multiplication Property of Equality.
In conclusion, if [tex]\( x = y \)[/tex], then [tex]\( x \cdot z = y \cdot z \)[/tex] represents the Multiplication Property of Equality.
