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1‐2: PROPERTIES OF REAL NUMBERS

Mr. GalloAlgebra 2

Real Number Review

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Subsets of the Real Numbers

Classifying Variables

Example 1: What set of numbers would best describe the number of participants in a race?

Example 2: What if each participant made a donation dof $15.50 to a local charity, which subset of real numbers best describes the amount of money raised?

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Graphing Real Numbers

What is the graph of the numbers :  5 , 2,2.62

2 640‐2‐4‐6

Ordering Real Numbers

How do  compare?

17 &3.8

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Properties of Real Numbers

Properties of Real NumbersProperties of Real Numbers

Let a, b and c represent real numbers

Property Addition Multiplication

Closure

Commutative

Associative

Identity

Inverse

Distributive

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Examples: Which property does the equation illustrate?

A.

B.

C.

2 31

3 2

3 4 5 4 3 5

3 2 3 3 2g h g g h g

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1-3: Algebraic ExpressionsMr. GalloAlgebra2

Modeling Words with an Algebraic Expression

What algebraic expression models the word phrase seven fewer than a number t?

What algebraic expression models the word phrase two times the sum of a and b?

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Modeling a SituationYou are on a bicycle trip. You traveled 52 miles the first day. Since then, your average rate has been 12 miles per hour. What algebraic expression models the distance you traveled so far?

Evaluating Algebraic Expressions

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What is the value of the expression for the given values of the variables?

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Writing and Evaluating an ExpressionTicket prices for admission to a museum are $8 for adults, $5 for children and $6 for seniors.a. What algebraic expression models the total number of dollars

collected in ticket sales?b. If 20 adult tickets, 16 children’s tickets and 10 senior tickets are sold

one morning, how much money is collected in all?

Vocabulary

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◦

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Properties for Simplifying Algebraic ExpressionsLet a, b and c represent real numbers:

Definition of Subtraction

Definition of Division

Distributive Property for Subtraction

Multiplication by 0

Multiplication by -1

Opposite of a Sum

Opposite of a Difference

Opposite of a Product

Opposite of an Opposite

Simplifying Algebraic Expressions Combine like terms. What is a simpler form of each expression?

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1-4: Solving Equations

Mr. GalloAlgebra 2

Review of Properties

Properties of EqualityAssume a, b and c represent real numbers.

Property Definition Example

Reflexive

Symmetric

Transitive

Substitution

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Review of Properties cont.

Properties of EqualityAssume a, b and c represent real numbers.

Property Definition Example

Addition

Subtraction

Multiplication

Division

Solving equations with more than one operation (variables on both sides)

1)

2)

3)

4)

5)

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Example 2: Solve the following equation

2 1 16y y

Ex. 5: If $1000 is in a bank account earning 5% simple interest, the dollar value of the account A in t years is given by . What is t in terms of A? 1000 1 0.05A t

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M R . G A L L O

A L G E B R A 2

1-5: Solving Inequalities

Equations

What is an inequality?

What is the solution to an inequality?

How do I know when to use an inequality?

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Writing an Inequality from a Sentence

1. The quotient of a number and 3 is no more than 15

2. The product of 7 and a number is more than 50

Writing and Graphing Inequalities

Inequality Word Sentence Graph

4x

4x

4x

4x

2 640‐2‐4‐6

2 640‐2‐4‐6

2 640‐2‐4‐6

2 640‐2‐4‐6

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Review of Properties

Properties of InequalitiesAssume a, b, c and d represent real numbers.

Property Definition Example

Transitive

Addition

Subtraction

Review of Properties cont.

Properties of InequalitiesAssume a, b, c and d represent real numbers.

Property Definition Example

Multiplication

Division

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Solving & Graphing Inequalities

1)

2)

3)

4)

5)

Example 1: Solve and graph the following inequality

4 7 20x

2

2 9 5 3x

‐8

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Using an Inequality

Plumber A charges $75 for a service charge and $40 per hour. Plumber B charges $50 per hour but no service charge. How many hours must a plumbing job last for Plumber A to cost less than Plumber B?

Example 2: Complete Got It? #3 on p.35 in your book

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9 5 4x x 3 3 3 2x x

Compound Inequalities

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Solving an “and” Inequality

What is the solution of and ? Graph the solution.32

a 3 5 8a

2 640‐2‐4‐6

Solving an “or” Inequality

What is the solution of or ? Graph the solution.

5 2 21m 4 1 21m

0 42-2‐4‐6‐8

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Mr. GalloAlgebra 2

0 5-5

What is the Absolute Value of a real number?◦

Characteristics:◦

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2 640‐2‐4‐6

What is the solution of Graph the solution

What is the solution of:2 5 9x

13 6 2 5

3x

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What are the solutions for ? 5x

2 640‐2‐4‐6

2-1

4 3 5x

4 3 5x

‐2 10

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2 640‐2‐4‐6

What are the solutions for ? 5x

2 6 10x

2 6 10x

0 42-2‐4‐6‐8

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Solutions of Absolute Values

Symbols Definition Graph

x a

x ax a

x ax a