Introduction to Algebra

Chapter Out line

□ Introduction to Variables
□ Solving Equations : The Addition Property
□ Solving Equations: The Multiplication Property
□ Solving Equations Using Addition and Multiplication Properties
□ Equations and Problem Solving

§11.1
Introduction to Variables

Section Objectives

□ Evaluating Algebraic Expressions
□  Combining Like Terms
□  Multiplying Expressions

Evaluating Algebraic Expressions

Combining Like Terms

EXAMPLE
Simplify 8y + 3y.

SOLUTION

Multiplying Expressions

EXAMPLE
Multiply:4(5y-6)

SOLUTION

§11.2
Solving Equations: The Addition Property

Section Objectives

□ Determining Whether a Number is a Solution
□ Using the Addition Property to Solve Equations

Determining Whether a Number is a Solution

Using the Addition Property to Solve Equations

EXAMPLE
Solve: f + 4 = -66

SOLUTION

§11.3
Solving Equations: The Multiplication Property

Section Objectives

□ Using the Multiplication Property to Solve Equations

Using the Multiplication Property to Solve
Equations

EXAMPLE
Solve: 7y = 21.

SOLUTION

§11.4
Solving Equations Using Addition and Multiplication Properties

Section Objectives

□ Solving Equations Using Addition and Multiplication Properties
□ Solving Equations Containing Parentheses
□ Writing Sentences as Equations

Solving Equations Using Addition and
Multiplication Properties

EXAMPLE
Solve: 3y – 12 = 0.

SOLUTION

Solving Equations Containing Parentheses

Steps	Example
Step 1: If parentheses are present, use the distributive property.	Solve: 3(x-1) = 12
Step 2: Combine any like terms on each side of the equation.
Step 3: Use the addition property of equality to rewrite the equation so that variable terms are on one side of the equation and constant terms are on the other side.
Step 4: Use the multiplication property of equality to divide both sides by the numerical coefficient of the variable to solve for.
Step 5: Check the solution in the original equation.

Writing Sentences as Equations

Key Words or Phrases	Examples	Symbols
equals	3 equals 2 plus 1	3 = 2 + 1
gives	the quotient of 10 and -5 gives -2
is/was	17 minus 12 is 5	17 –12 = 5
yields	11 plus 2 yields 13	11 + 2 = 13
amounts to	twice -15 amounts to -30	2(-15) = -30
is equal to	-24 is equal to 2 times -12	-24 = 2(-12)

Writing Sentences as Equations

EXAMPLE
Write the fol lowing sentence as an equation:
The product of -5 and -29 gives 145.

SOLUTION

§11.5
Equations and Problem Solving

Section Objectives

□ Writing Phrases as Algebraic Expressions
□ Writing Sentences as Equations
□ Using Problem-Solving Steps to Solve Problems

Writing Phrases as Algebraic Expressions

EXAMPLE
Write the following phrase as a variable expression:
Ten plus a number

SOLUTION

Writing Sentences as Equations

EXAMPLE
Write the following sentence as an equation:
Five subtracted from a number equals 10.

SOLUTION

Using Problem-Solving Steps to Solve Problems

EXAMPLE
The sum of 7, 9, and a number is 40. Find the number  UNDERSTAND

SOLUTION

The unknown number is 24.