Properties of equality
We will show 8 properties of equality. When appropriate, we will illustrate with real life examples of properties of equality. Let x, y, and z represent real numbers.
Reflexive property: x = x
Example:
2 = 2
I am equal to myself
1020 = 1020
Symmetric property: If x = y, then y = x
Example:
If fish = tuna, then tuna = fish
If x + 8 = 6, then 6 = x = 8
transitive property: If x = y and y = z, then x = z
Example:
If John's height = Mary's height and Mary's height = Peter's height, then John's height = Peter's height
If 2x + 8 = 12 and 12 = x  2, then 2x + 8 = x  2
Addition property: If x = y, then x + z = y + z
Example:
If John's height = Mary's height, then John's height + 2 = Mary's height + 2
If 5 = 5, then 5 + 3 = 5 + 3
If x + 2 = 5, then x + 2 + 2 = 5 + 2
Subtraction property: If x = y, then x − z = y − z
Example:
If John's height = Mary's height, then John's height − 5 = Mary's height − 5
If 8 = 8, then 8 − 3 = 8 − 3
If 2y + 4 = 10, then 2y + 4  4 = 10  4
Multiplication property: If x = y, then x × z = y × z
Example: Suppose Jetser's weight = Darline's weight, then Jetser's weight × 4 = Darline's weight × 4
Or suppose 10 = 10, then 10 × 10 = 10 × 10
Division property: If x = y, then x ÷ z = y ÷ z
Example: Suppose Jetser's weight = Darline's weight, then Jetser's weight ÷ 4 = Darline's weight ÷ 4
Or suppose 20 = 20, then 20 ÷ 10 = 20 ÷ 10
Substitution property: If x = y, then y can be substituted for x in any expression
Example: x = 2 and x + 5 = 7, then 2 can be substituted in x + 5 = 7 to obtain 2 + 5 = 7
Any questions about the properties of equality, let me know.
Here is a summary of the properties of equality

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