Linear and Quadratic Functions: Solving Linear Equations and Inequalities

Properties of Equality

Before we can start solving linear equations it is important to go over the Properties of Equality. Look over the following list:

For real numbers a, b, and c:

Reflexive Property	a = a
Symmetric Property	If a = b, then b = a
Transitive Property	If a = b and b = c, then a = c
Addition Property	If a = b, then a + c = b + c
Subtraction Property	If a = b, then a – c = b – c
Multiplication Property	If a = b, then ac = bc
Division Property	If a = b, then , where c ≠ 0

Scales, representing balance We are going to be using these properties as we solve linear equations and inequalities. The key to solving linear equations is to think of a balance. If you put something or take something away from one side, you must do the same to the other. For example, look at the Subtraction Property. Notice that c is subtracted from both sides of the equation, to keep the balance even. Let’s call this balance the Algebraic Balance.