Algebra chapter 3

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Algebra chapter 3

• Solving and Graphing Linear Inequalities

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One-step linear inequalities3.1
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Vocabulary

• An equation is formed when an equal sign () is
  placed between two expressions creating a left
  and a right side of the equation
• An equation that contains one or more variables
  is called an open sentence
• When a variable in a single-variable equation is
  replaced by a number the resulting statement can
  be true or false
• If the statement is true, the number is a
  solution of an equation
• Substituting a number for a variable in an
  equation to see whether the resulting statement
  is true or false is called checking a possible
  solution

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Inequalities

• Another type of open sentence is called an
  inequality.
• An inequality is formed when and inequality sign
  is placed between two expressions
• A solution to an inequality are numbers that
  produce a true statement when substituted for the
  variable in the inequality

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Inequality Symbols

• Listed below are the 4 inequality symbols and
  their meaning
• lt Less than
• Less than or equal to
• gt Greater than
• Greater than or equal to

Note We will be working with inequalities
throughout this courseand you are expected to
know the difference between equalities and
inequalities
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Graphs of linear inequalities

• Graph (1 variable)
• The set of points on a number line that
  represents all solutions of the inequality

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Graphs of linear inequalities

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Graphs of linear inequalities

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Writing linear inequalities

• Bob hopes that his next math test grade will be
  higher than his current average. His first three
  test scores were 77, 83, and 86.
• Why would an inequality be best in this case?
• How can we come up with this inequality?
• Graph! ?

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Solving one-step linear inequalities

• Equivalent Inequalities
• Two or more inequalities with exactly the same
  solution
• Manipulating Inequalities
• All of the same rules apply to inequalities as
  equations
• When multiplying or dividing by a negative
  number, we have to switch the inequality!
• Less than becomes greater than, etc.

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Solving with addition/subtraction

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Solving with addition/subtraction

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Solving with multiplication/division

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Solving with multiplication/division

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Why do we have to change the sign?

• Is there another way we can solve this?

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Solving multi-step linear inequalities3.2
Algebra chapter 3

• Solving and Graphing Linear Inequalities

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Multi step inequalities

• Treat inequalities just like you would normal,
  everyday equations
• change the sign when multiplying or dividing by
  a negative!!

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Examples
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Examples
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Examples
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Examples
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Example

• You plan to publish an online newsletter that
  reports the results of snow cross competitions.
  You do not want your monthly costs to exceed
  2370. Your fixed monthly costs are 1200. You
  must also pay 130 per month to each article
  writer. How many writers can you afford to hire
  in a month?

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Examples Try these on your own!



 
 
 
 
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1) Which graph represents the correct answer to
gt 1

?
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2) When solving gt -10will the inequality
switch?

1. Yes!
2. No!
3. I still dont know!

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3) When solving will the inequality switch?

1. Yes!
2. No!
3. I still dont know!

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4) Solve -8p -96

1. p 12
2. p -12
3. p 12
4. p -12

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5) Solve 7v lt -105

?
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Class workp.343 15-37 oddIf you do not
finish in class, then it becomes homework!
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Compound inequalities3.6
Algebra chapter 3

• Solving and Graphing Linear Inequalities

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Compound inequality

• What does compound mean?
• Compound fracture?
• Sowhats a compound inequality?
• An inequality consisting of two inequalities
  connected by an and or an or

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Graphing Compound Inequalities

• Graph the following

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Graphing Compound Inequalities

• Graph the following

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Graphing Compound Inequalities

• Graph the following
• All real numbers that are greater than or equal
  to -2 and less than 3

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Solving Compound inequalities

• Again.treat these like equations!
• Whenever we do something to one side
• We do it to every side!

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Solving Compound Inequalities
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Solving Compound Inequalities
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Solving Compound Inequalities
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Solving Compound Inequalities
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homeworkp.349 12-36 even
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Solving Absolute-Value Equations and
Inequalities3.6 (Day 1)
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Abs. Value

• What is Absolute Value?
• Distance from zero
• What does that mean?

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Abs. Value

• So.an absolute value equation has how many
  solutions?
• Is this always true?

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Abs. Value

• How do we apply this to equations?
• Ex

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Examples
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Examples
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Examples
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Examples
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Examples
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p.35619-36
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Solving Absolute-Value Equations and
Inequalities3.6 (Day 2)
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Absolute Value and Inequalities
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Absolute Value and Inequalities
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Examples
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Examples
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Examples