PROPERTIES OF EQUALITY
These three properties define an equivalence relation
Reflexive Property
For all real numbers x,
x = x.
A number equals itself.
Symmetric Property
For all real numbers x and y,
if x = y, then y = x.
Order of equality does not matter.
Transitive Property
For all real numbers
x, y, and z,
if x = y and y = z, then x = z.
Two numbers equal to the same number are equal to each other.
These properties allow you to balance and solve equations involving real numbers
Addition Property
For all real numbers
x, y, and z,
if x = y, then x + z = y + z.
Subtraction Property
For all real numbers
x, y, and z,
if x = y, then x − z = y − z .
Multiplication Property
For all real numbers
x, y, and z,
if x = y, then xz = yz.
Division Property
For all real numbers
x, y, and z,
if x = y, and z ≠ 0,
then x/z = y/z.
Substitution Property
For all real numbers x and y,
if x = y, then y can be substituted for x in any expression.
These three properties define an equivalence relation
Reflexive Property
For all real numbers x,
x = x.
A number equals itself.
Symmetric Property
For all real numbers x and y,
if x = y, then y = x.
Order of equality does not matter.
Transitive Property
For all real numbers
x, y, and z,
if x = y and y = z, then x = z.
Two numbers equal to the same number are equal to each other.
These properties allow you to balance and solve equations involving real numbers
Addition Property
For all real numbers
x, y, and z,
if x = y, then x + z = y + z.
Subtraction Property
For all real numbers
x, y, and z,
if x = y, then x − z = y − z .
Multiplication Property
For all real numbers
x, y, and z,
if x = y, then xz = yz.
Division Property
For all real numbers
x, y, and z,
if x = y, and z ≠ 0,
then x/z = y/z.
Substitution Property
For all real numbers x and y,
if x = y, then y can be substituted for x in any expression.