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ALGEBRA POSTULATES

Postulate of Equality
Reflexive Property of Equality:	a = a
Symmetric Property of Equality:	if a = b, then b = a
Transitive Property of Equality:	if a = b and b = c, then a = c
Postulates of Equality and Operations
Addition Property of Equality:	if a = b, then a + c = b + c
Multiplication Property of Equality:	if a = b, then a * c = b * c
Substitution Property of Equality:	if a = b, then a can be substituted for b in any equation or inequality
Subtraction Property of Equality:	if a = b, then a - c = b - c
Postulates of Inequality and Operations
Addition Property of Inequality:	if a < > b, then a + c < > b + c
Multiplication Property of Inequality:	if a < b and c > 0, then a * c < b * c if a < b and c < 0, then a * c > b * c
Equation to Inequality Property:	if a and b are positive, and a + b = c, then c > a and c > b if a and b are negative, and a + b = c, then c < a and c < b
Subtraction Property of Inequality:	if a < > b, then a - c < > b - c
Transitive Property of Inequality:	if a < b and b < c, then a < c
Postulates of Operation
Commutative Property of Addition:	a + b = b + a
Commutative Property of Multiplication:	a * b = b * a
Distributive Property:	a * (b + c) = a * b + a * c and vice versa

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