# Algebra Postulates

Here are the basic postulates of equality, inequality, and operations. Dave didn't get a chance to write them, and I needed them for my section on the basic postulates of Geometry (review is always good). Have a blast!

.

## Postulates 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