Author: mark_cameron
Last saved by: MHE
Company: McGraw-Hill

Lesson 1-2

Example 1 Evaluate Algebraic Expressions
Evaluate 3x – 2y + 5 if x = 3 and y = 2.

3x – 2y + 5 = 3(3) – 2(2) + 5		Replace x with 3 and y with 2.
	= 9 – 4 + 5		Do all multiplications first.
	= 5 + 5			Add and subtract in order from left to right.
	= 10

Example 2 Evaluate Algebraic Expressions
Evaluate m^2 – 4m + 6 if m = 2.

m^2 – 4m + 6 	= (2)^2 – 4(2) + 6		Replace m with 2.
		= 4 – 8 + 6		Evaluate powers before other operations.
		= –4 + 6			Add and subtract in order from left to right.
		= 2

Example 3 Evaluate Algebraic Fractions
Evaluate  if x = 3 and z = 6.

 	= 		Replace x with 3 and z with 6.
	= 		Evaluate the power in the numerator. 3^3 = 3 ∙ 3 ∙ 3 or 27
	= 			Subtract in the denominator. Then divide.
	= 9

Example 4 Identify Properties
Name the property shown by the statement 3 + 0 = 3.

By adding zero, the number stays the same. This is the Identity Property of Addition.

Example 5 Find a Counterexample
State whether the following conjecture is true or false. If false, provide a counterexample.
Subtraction of whole numbers is commutative.

Write two subtraction expressions using the Commutative Property, and then check to see whether they are equal.

6 – 2  2 – 6		State the conjecture.
      4  –4		Subtract.

We found a counterexample. That is, 6 – 2  2 – 6.
So, subtraction of whole numbers is not commutative. The conjecture is false.