SlideShare una empresa de Scribd logo
1 de 20
Descargar para leer sin conexión
Monday, October 21, 2032

Today:
Warm-Up (4)
Inequalities
Class Work
Warm-Up Questions

1.

Order of Operations:
18 - (4 + 2 * 3) + 12
18 - (10) + 12; 8 + 12 = 20

2. (6+(9−5×3))×4
=(8+(3−40))×4; =(8+(−37))×4;
=(−29)×4; = -116
3. -13 x = - 13
10

Multiply each side by - 10
13x = 130; x = 10
Warm-Up Questions

4. 3|x - 3|+ 5 = - 2|x - 3| + 9
= 3|x - 3|+ 2|x - 3|= 5|x - 3|+ 5 = 9
5|x - 3|= 4; x - 3 = 4/5, -4/5
x = 4/5 + 15/5; x = 19/5
x = -4/5 + 15/5; x = 11/5
Introduction
to
Inequalities
Understanding
&
Solutions
Inequalities
 The

Prefix 'in' means not. Incorrect, Inflexible
 Equations which have solutions are equal to a
specific value, or number: 2x = 8 can only
equal 4; no other number will satisfy this
equation.
 Inequalities, however, can have many answers.
They are not equal to a specific value.
 When solving inequalities, we are solving for a
range of numbers, not just one.
 Let's look at some examples of inequalities
Inequalities
Look at, and think about, the following signs:

The problem is, none of these signs say what
they're really supposed to say. Not only that,
they are all incorrect. To be correct, they needed
to include an inequality.
Inequalities
Let's put this sign in mathematical terms:
Let h = the height required to use the ride. The sign
says you must be 46" tall, therefore h = 46"
According to the sign, if you're not 46" tall, you cannot
ride. But how many people are exactly 46" tall?
What they really meant to say was...
You must be at least 46" tall, or in
mathematical terms...
Your height must be equal to or
greater than 46". This is our
inequality. Our solution is not a
single number, but a range of
numbers.
Inequalities
This sign obviously refers to the drinking age. But
the sign states that even 22 year olds, or 75 year
old people cannot enter. The two words missing
here are: at least
In mathematical terms, the drinking age is:
Equal to or greater than 21
d > 21
Inequalities
As far as the signs are written:

Incorrect

Correct
Inequalities
Incorrect

Correct
Solving Inequalities
The process of solving Inequalities is the same as
equations except for one rule(which we'll get to
later), and how inequalities are shown graphically.

Less Than; shown with an open circle on
number line; x < -4

Less Than or equal to; shown with closed
circle on number line; x < -4
Solving Inequalities

Greater Than; shown with an open circle
on number line; x > -4

Greater Than or equal to; shown with a
closed circle on number line; x < -4
Solving Inequalities

Basic Inequalities
1. Write the inequality shown below
x<3

x>0

-5 < x < 2
Inequalities
Graphing Inequalities
Draw a number line and graph the following:
1. 1 <x < 8
2, -2 < x < -1
3. -5 < x
<2
Solving Inequalities
Solve for x and Graph

1. 6x - 7 < 5

1. x < 2; Graph

2. 4(x - 2) > 20

x>3

3. x - 8 < - 6

x<2

And now the one difference between equations &
inequalities:

Solve for x and Graph
4. -2x < 4; When multiplying or dividing by a negative
coefficient, you must switch the sign

4. -2x < 4; -2x/-2 > 4/-2; x > -2
Inequalities
Think about the rule for example 4 with numbers in there,
instead of variables. -2 < 4
You know that the number four is larger than the number
negative two: 4 > -2.
Multiplying through this inequality by –1, we get –4 < –
2, which the number line shows is true:

If we hadn't flipped the inequality, we would have ended
up with "–4 > –2", which clearly isn't true.
When multiplying or dividing a negative coefficient,
you must flip the sign for the inequality to remain true.
Solving Inequalities
Last 2 Practice Problems;
Solve & Graph on Number Line

5. x - 12 < -6
5. x - 12 < -6;
+12 +12

6. 6 - 2x > - x
+2x +2x
6 > x; x < 6

6. 6 - 2x > - x
5. x < 6;
Today:

Class Work:
5-1: All
5-2: All
October 21, 2013
Inequalities

Más contenido relacionado

La actualidad más candente

Absolute Value Notes
Absolute Value NotesAbsolute Value Notes
Absolute Value Notesmpscils598s07
 
Tues. 25 sept
Tues. 25 septTues. 25 sept
Tues. 25 septkhyps13
 
Non verbal reasoning
Non  verbal reasoningNon  verbal reasoning
Non verbal reasoningindu thakur
 
Solving Inequalities Lesson
Solving Inequalities LessonSolving Inequalities Lesson
Solving Inequalities LessonSpainhour
 
Simplifying basic radical expressions 2
Simplifying basic radical expressions 2Simplifying basic radical expressions 2
Simplifying basic radical expressions 2DaisyListening
 
Divisibility rules for 3,6,& 9
Divisibility rules for 3,6,& 9Divisibility rules for 3,6,& 9
Divisibility rules for 3,6,& 9Mary Capuyan
 
Adding Mixed Numbers
Adding Mixed NumbersAdding Mixed Numbers
Adding Mixed NumbersDan O'Brien
 
Questions on Verbal & Non Verbal Reasoning
Questions on Verbal & Non Verbal ReasoningQuestions on Verbal & Non Verbal Reasoning
Questions on Verbal & Non Verbal ReasoningLearnPick
 
Mathematical Operations Reasoning Questions
Mathematical Operations Reasoning QuestionsMathematical Operations Reasoning Questions
Mathematical Operations Reasoning QuestionsSandip Kar
 
Multiplying binomials and trinomials
Multiplying binomials and trinomialsMultiplying binomials and trinomials
Multiplying binomials and trinomials40388915
 
Associative Property
Associative PropertyAssociative Property
Associative Propertyhiratufail
 
Lattice multiplication
Lattice multiplicationLattice multiplication
Lattice multiplicationbrizett45
 
Unit 3 review
Unit 3 reviewUnit 3 review
Unit 3 reviewMs. Jones
 

La actualidad más candente (19)

Absolute Value Notes
Absolute Value NotesAbsolute Value Notes
Absolute Value Notes
 
PEMDAS
PEMDASPEMDAS
PEMDAS
 
Tues. 25 sept
Tues. 25 septTues. 25 sept
Tues. 25 sept
 
Non verbal reasoning
Non  verbal reasoningNon  verbal reasoning
Non verbal reasoning
 
Divisibility rule
Divisibility ruleDivisibility rule
Divisibility rule
 
Solving Inequalities Lesson
Solving Inequalities LessonSolving Inequalities Lesson
Solving Inequalities Lesson
 
Simplifying basic radical expressions 2
Simplifying basic radical expressions 2Simplifying basic radical expressions 2
Simplifying basic radical expressions 2
 
Divisibility rules for 3,6,& 9
Divisibility rules for 3,6,& 9Divisibility rules for 3,6,& 9
Divisibility rules for 3,6,& 9
 
Adding Mixed Numbers
Adding Mixed NumbersAdding Mixed Numbers
Adding Mixed Numbers
 
Math trick
Math trickMath trick
Math trick
 
Math Trick
Math TrickMath Trick
Math Trick
 
Developing strategic intervention material
Developing strategic intervention materialDeveloping strategic intervention material
Developing strategic intervention material
 
Questions on Verbal & Non Verbal Reasoning
Questions on Verbal & Non Verbal ReasoningQuestions on Verbal & Non Verbal Reasoning
Questions on Verbal & Non Verbal Reasoning
 
Mathematical Operations Reasoning Questions
Mathematical Operations Reasoning QuestionsMathematical Operations Reasoning Questions
Mathematical Operations Reasoning Questions
 
Multiplying binomials and trinomials
Multiplying binomials and trinomialsMultiplying binomials and trinomials
Multiplying binomials and trinomials
 
Associative Property
Associative PropertyAssociative Property
Associative Property
 
Lattice multiplication
Lattice multiplicationLattice multiplication
Lattice multiplication
 
Unit 3 review
Unit 3 reviewUnit 3 review
Unit 3 review
 
[000048]
[000048][000048]
[000048]
 

Similar a October 21, 2013

Similar a October 21, 2013 (20)

Inequalities mathematics grade nine igcse.ppt
Inequalities mathematics grade nine igcse.pptInequalities mathematics grade nine igcse.ppt
Inequalities mathematics grade nine igcse.ppt
 
November 6th, 2014
November 6th, 2014November 6th, 2014
November 6th, 2014
 
Resolver inecuaciones 2009.pdf
Resolver inecuaciones 2009.pdfResolver inecuaciones 2009.pdf
Resolver inecuaciones 2009.pdf
 
inequalities
 inequalities inequalities
inequalities
 
AFS7 Math 3
AFS7 Math 3AFS7 Math 3
AFS7 Math 3
 
AFS7 Math 3
AFS7 Math 3AFS7 Math 3
AFS7 Math 3
 
AFS7 Math1
AFS7 Math1AFS7 Math1
AFS7 Math1
 
AFS7 Math 3
AFS7 Math 3AFS7 Math 3
AFS7 Math 3
 
PEMDAS - The Proper Order of Mathematical Operations
PEMDAS - The Proper Order of Mathematical OperationsPEMDAS - The Proper Order of Mathematical Operations
PEMDAS - The Proper Order of Mathematical Operations
 
Solving inequalities
Solving inequalitiesSolving inequalities
Solving inequalities
 
Inequalities
InequalitiesInequalities
Inequalities
 
Solving Absolute Value Equations and Inequalities.ppt
Solving Absolute Value Equations and Inequalities.pptSolving Absolute Value Equations and Inequalities.ppt
Solving Absolute Value Equations and Inequalities.ppt
 
Solving and Graphing Inequalities.ppt
Solving and Graphing Inequalities.pptSolving and Graphing Inequalities.ppt
Solving and Graphing Inequalities.ppt
 
Solving Inequalitiesmath sixt grade ineq
Solving Inequalitiesmath sixt grade ineqSolving Inequalitiesmath sixt grade ineq
Solving Inequalitiesmath sixt grade ineq
 
Solving Inequalities.ppt
Solving Inequalities.pptSolving Inequalities.ppt
Solving Inequalities.ppt
 
Class Presentation Math 1
Class Presentation Math 1Class Presentation Math 1
Class Presentation Math 1
 
Chapter 1 Study Guide
Chapter 1  Study  GuideChapter 1  Study  Guide
Chapter 1 Study Guide
 
Chapter 1 Study Guide
Chapter 1  Study  GuideChapter 1  Study  Guide
Chapter 1 Study Guide
 
CBSE Class XI Maths Linear inequalities
CBSE Class XI Maths Linear inequalitiesCBSE Class XI Maths Linear inequalities
CBSE Class XI Maths Linear inequalities
 
6 4 Absolute Value And Graphing
6 4 Absolute Value And Graphing6 4 Absolute Value And Graphing
6 4 Absolute Value And Graphing
 

Más de khyps13

August 23, 2016
August 23, 2016August 23, 2016
August 23, 2016khyps13
 
August 22, 2016
August 22, 2016August 22, 2016
August 22, 2016khyps13
 
August 19, 2016
August 19, 2016August 19, 2016
August 19, 2016khyps13
 
August 18, 2016
August 18, 2016August 18, 2016
August 18, 2016khyps13
 
Aug 17, 2016
Aug 17, 2016Aug 17, 2016
Aug 17, 2016khyps13
 
Ultimate guide to systems of equations
Ultimate guide to systems of equationsUltimate guide to systems of equations
Ultimate guide to systems of equationskhyps13
 
March 29, 2016
March 29, 2016March 29, 2016
March 29, 2016khyps13
 
March 28, 2016
March 28, 2016March 28, 2016
March 28, 2016khyps13
 
March 31, 2016
March 31, 2016March 31, 2016
March 31, 2016khyps13
 
March 30, 2016
March 30, 2016March 30, 2016
March 30, 2016khyps13
 
March 21, 2016
March 21, 2016March 21, 2016
March 21, 2016khyps13
 
April 5, 2016
April 5, 2016April 5, 2016
April 5, 2016khyps13
 
April 4, 2016
April 4, 2016April 4, 2016
April 4, 2016khyps13
 
April 6, 2016
April 6, 2016April 6, 2016
April 6, 2016khyps13
 
April 1, 2016
April 1, 2016April 1, 2016
April 1, 2016khyps13
 
February 17 2015
February 17 2015February 17 2015
February 17 2015khyps13
 
February 18 2016
February 18 2016February 18 2016
February 18 2016khyps13
 
February 16 2016
February 16 2016February 16 2016
February 16 2016khyps13
 
February 9 2016
February 9 2016February 9 2016
February 9 2016khyps13
 
February 10 2016
February 10 2016February 10 2016
February 10 2016khyps13
 

Más de khyps13 (20)

August 23, 2016
August 23, 2016August 23, 2016
August 23, 2016
 
August 22, 2016
August 22, 2016August 22, 2016
August 22, 2016
 
August 19, 2016
August 19, 2016August 19, 2016
August 19, 2016
 
August 18, 2016
August 18, 2016August 18, 2016
August 18, 2016
 
Aug 17, 2016
Aug 17, 2016Aug 17, 2016
Aug 17, 2016
 
Ultimate guide to systems of equations
Ultimate guide to systems of equationsUltimate guide to systems of equations
Ultimate guide to systems of equations
 
March 29, 2016
March 29, 2016March 29, 2016
March 29, 2016
 
March 28, 2016
March 28, 2016March 28, 2016
March 28, 2016
 
March 31, 2016
March 31, 2016March 31, 2016
March 31, 2016
 
March 30, 2016
March 30, 2016March 30, 2016
March 30, 2016
 
March 21, 2016
March 21, 2016March 21, 2016
March 21, 2016
 
April 5, 2016
April 5, 2016April 5, 2016
April 5, 2016
 
April 4, 2016
April 4, 2016April 4, 2016
April 4, 2016
 
April 6, 2016
April 6, 2016April 6, 2016
April 6, 2016
 
April 1, 2016
April 1, 2016April 1, 2016
April 1, 2016
 
February 17 2015
February 17 2015February 17 2015
February 17 2015
 
February 18 2016
February 18 2016February 18 2016
February 18 2016
 
February 16 2016
February 16 2016February 16 2016
February 16 2016
 
February 9 2016
February 9 2016February 9 2016
February 9 2016
 
February 10 2016
February 10 2016February 10 2016
February 10 2016
 

Último

To Create Your Own Wig Online To Create Your Own Wig Online
To Create Your Own Wig Online  To Create Your Own Wig OnlineTo Create Your Own Wig Online  To Create Your Own Wig Online
To Create Your Own Wig Online To Create Your Own Wig Onlinelng ths
 
Live-Streaming in the Music Industry Webinar
Live-Streaming in the Music Industry WebinarLive-Streaming in the Music Industry Webinar
Live-Streaming in the Music Industry WebinarNathanielSchmuck
 
TalentView Webinar: Empowering the Modern Workforce_ Redefininig Success from...
TalentView Webinar: Empowering the Modern Workforce_ Redefininig Success from...TalentView Webinar: Empowering the Modern Workforce_ Redefininig Success from...
TalentView Webinar: Empowering the Modern Workforce_ Redefininig Success from...TalentView
 
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptxHELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptxHelene Heckrotte
 
IIBA® Melbourne - Navigating Business Analysis - Excellence for Career Growth...
IIBA® Melbourne - Navigating Business Analysis - Excellence for Career Growth...IIBA® Melbourne - Navigating Business Analysis - Excellence for Career Growth...
IIBA® Melbourne - Navigating Business Analysis - Excellence for Career Growth...AustraliaChapterIIBA
 
BCE24 | Virtual Brand Ambassadors: Making Brands Personal - John Meulemans
BCE24 | Virtual Brand Ambassadors: Making Brands Personal - John MeulemansBCE24 | Virtual Brand Ambassadors: Making Brands Personal - John Meulemans
BCE24 | Virtual Brand Ambassadors: Making Brands Personal - John MeulemansBBPMedia1
 
Michael Vidyakin: Introduction to PMO (UA)
Michael Vidyakin: Introduction to PMO (UA)Michael Vidyakin: Introduction to PMO (UA)
Michael Vidyakin: Introduction to PMO (UA)Lviv Startup Club
 
Upgrade Your Banking Experience with Advanced Core Banking Applications
Upgrade Your Banking Experience with Advanced Core Banking ApplicationsUpgrade Your Banking Experience with Advanced Core Banking Applications
Upgrade Your Banking Experience with Advanced Core Banking ApplicationsIntellect Design Arena Ltd
 
7movierulz.uk
7movierulz.uk7movierulz.uk
7movierulz.ukaroemirsr
 
MC Heights construction company in Jhang
MC Heights construction company in JhangMC Heights construction company in Jhang
MC Heights construction company in Jhangmcgroupjeya
 
Borderless Access - Global Panel book-unlock 2024
Borderless Access - Global Panel book-unlock 2024Borderless Access - Global Panel book-unlock 2024
Borderless Access - Global Panel book-unlock 2024Borderless Access
 
Chicago Medical Malpractice Lawyer Chicago Medical Malpractice Lawyer.pdf
Chicago Medical Malpractice Lawyer Chicago Medical Malpractice Lawyer.pdfChicago Medical Malpractice Lawyer Chicago Medical Malpractice Lawyer.pdf
Chicago Medical Malpractice Lawyer Chicago Medical Malpractice Lawyer.pdfSourav Sikder
 
Building Your Personal Brand on LinkedIn - Expert Planet- 2024
 Building Your Personal Brand on LinkedIn - Expert Planet-  2024 Building Your Personal Brand on LinkedIn - Expert Planet-  2024
Building Your Personal Brand on LinkedIn - Expert Planet- 2024Stephan Koning
 
PDT 88 - 4 million seed - Seed - Protecto.pdf
PDT 88 - 4 million seed - Seed - Protecto.pdfPDT 88 - 4 million seed - Seed - Protecto.pdf
PDT 88 - 4 million seed - Seed - Protecto.pdfHajeJanKamps
 
Anyhr.io | Presentation HR&Recruiting agency
Anyhr.io | Presentation HR&Recruiting agencyAnyhr.io | Presentation HR&Recruiting agency
Anyhr.io | Presentation HR&Recruiting agencyHanna Klim
 
PDT 89 - $1.4M - Seed - Plantee Innovations.pdf
PDT 89 - $1.4M - Seed - Plantee Innovations.pdfPDT 89 - $1.4M - Seed - Plantee Innovations.pdf
PDT 89 - $1.4M - Seed - Plantee Innovations.pdfHajeJanKamps
 
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003believeminhh
 
Ethical stalking by Mark Williams. UpliftLive 2024
Ethical stalking by Mark Williams. UpliftLive 2024Ethical stalking by Mark Williams. UpliftLive 2024
Ethical stalking by Mark Williams. UpliftLive 2024Winbusinessin
 
Entrepreneurship & organisations: influences and organizations
Entrepreneurship & organisations: influences and organizationsEntrepreneurship & organisations: influences and organizations
Entrepreneurship & organisations: influences and organizationsP&CO
 
Talent Management research intelligence_13 paradigm shifts_20 March 2024.pdf
Talent Management research intelligence_13 paradigm shifts_20 March 2024.pdfTalent Management research intelligence_13 paradigm shifts_20 March 2024.pdf
Talent Management research intelligence_13 paradigm shifts_20 March 2024.pdfCharles Cotter, PhD
 

Último (20)

To Create Your Own Wig Online To Create Your Own Wig Online
To Create Your Own Wig Online  To Create Your Own Wig OnlineTo Create Your Own Wig Online  To Create Your Own Wig Online
To Create Your Own Wig Online To Create Your Own Wig Online
 
Live-Streaming in the Music Industry Webinar
Live-Streaming in the Music Industry WebinarLive-Streaming in the Music Industry Webinar
Live-Streaming in the Music Industry Webinar
 
TalentView Webinar: Empowering the Modern Workforce_ Redefininig Success from...
TalentView Webinar: Empowering the Modern Workforce_ Redefininig Success from...TalentView Webinar: Empowering the Modern Workforce_ Redefininig Success from...
TalentView Webinar: Empowering the Modern Workforce_ Redefininig Success from...
 
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptxHELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
 
IIBA® Melbourne - Navigating Business Analysis - Excellence for Career Growth...
IIBA® Melbourne - Navigating Business Analysis - Excellence for Career Growth...IIBA® Melbourne - Navigating Business Analysis - Excellence for Career Growth...
IIBA® Melbourne - Navigating Business Analysis - Excellence for Career Growth...
 
BCE24 | Virtual Brand Ambassadors: Making Brands Personal - John Meulemans
BCE24 | Virtual Brand Ambassadors: Making Brands Personal - John MeulemansBCE24 | Virtual Brand Ambassadors: Making Brands Personal - John Meulemans
BCE24 | Virtual Brand Ambassadors: Making Brands Personal - John Meulemans
 
Michael Vidyakin: Introduction to PMO (UA)
Michael Vidyakin: Introduction to PMO (UA)Michael Vidyakin: Introduction to PMO (UA)
Michael Vidyakin: Introduction to PMO (UA)
 
Upgrade Your Banking Experience with Advanced Core Banking Applications
Upgrade Your Banking Experience with Advanced Core Banking ApplicationsUpgrade Your Banking Experience with Advanced Core Banking Applications
Upgrade Your Banking Experience with Advanced Core Banking Applications
 
7movierulz.uk
7movierulz.uk7movierulz.uk
7movierulz.uk
 
MC Heights construction company in Jhang
MC Heights construction company in JhangMC Heights construction company in Jhang
MC Heights construction company in Jhang
 
Borderless Access - Global Panel book-unlock 2024
Borderless Access - Global Panel book-unlock 2024Borderless Access - Global Panel book-unlock 2024
Borderless Access - Global Panel book-unlock 2024
 
Chicago Medical Malpractice Lawyer Chicago Medical Malpractice Lawyer.pdf
Chicago Medical Malpractice Lawyer Chicago Medical Malpractice Lawyer.pdfChicago Medical Malpractice Lawyer Chicago Medical Malpractice Lawyer.pdf
Chicago Medical Malpractice Lawyer Chicago Medical Malpractice Lawyer.pdf
 
Building Your Personal Brand on LinkedIn - Expert Planet- 2024
 Building Your Personal Brand on LinkedIn - Expert Planet-  2024 Building Your Personal Brand on LinkedIn - Expert Planet-  2024
Building Your Personal Brand on LinkedIn - Expert Planet- 2024
 
PDT 88 - 4 million seed - Seed - Protecto.pdf
PDT 88 - 4 million seed - Seed - Protecto.pdfPDT 88 - 4 million seed - Seed - Protecto.pdf
PDT 88 - 4 million seed - Seed - Protecto.pdf
 
Anyhr.io | Presentation HR&Recruiting agency
Anyhr.io | Presentation HR&Recruiting agencyAnyhr.io | Presentation HR&Recruiting agency
Anyhr.io | Presentation HR&Recruiting agency
 
PDT 89 - $1.4M - Seed - Plantee Innovations.pdf
PDT 89 - $1.4M - Seed - Plantee Innovations.pdfPDT 89 - $1.4M - Seed - Plantee Innovations.pdf
PDT 89 - $1.4M - Seed - Plantee Innovations.pdf
 
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
 
Ethical stalking by Mark Williams. UpliftLive 2024
Ethical stalking by Mark Williams. UpliftLive 2024Ethical stalking by Mark Williams. UpliftLive 2024
Ethical stalking by Mark Williams. UpliftLive 2024
 
Entrepreneurship & organisations: influences and organizations
Entrepreneurship & organisations: influences and organizationsEntrepreneurship & organisations: influences and organizations
Entrepreneurship & organisations: influences and organizations
 
Talent Management research intelligence_13 paradigm shifts_20 March 2024.pdf
Talent Management research intelligence_13 paradigm shifts_20 March 2024.pdfTalent Management research intelligence_13 paradigm shifts_20 March 2024.pdf
Talent Management research intelligence_13 paradigm shifts_20 March 2024.pdf
 

October 21, 2013

  • 1. Monday, October 21, 2032 Today: Warm-Up (4) Inequalities Class Work
  • 2. Warm-Up Questions 1. Order of Operations: 18 - (4 + 2 * 3) + 12 18 - (10) + 12; 8 + 12 = 20 2. (6+(9−5×3))×4 =(8+(3−40))×4; =(8+(−37))×4; =(−29)×4; = -116 3. -13 x = - 13 10 Multiply each side by - 10 13x = 130; x = 10
  • 3. Warm-Up Questions 4. 3|x - 3|+ 5 = - 2|x - 3| + 9 = 3|x - 3|+ 2|x - 3|= 5|x - 3|+ 5 = 9 5|x - 3|= 4; x - 3 = 4/5, -4/5 x = 4/5 + 15/5; x = 19/5 x = -4/5 + 15/5; x = 11/5
  • 5. Inequalities  The Prefix 'in' means not. Incorrect, Inflexible  Equations which have solutions are equal to a specific value, or number: 2x = 8 can only equal 4; no other number will satisfy this equation.  Inequalities, however, can have many answers. They are not equal to a specific value.  When solving inequalities, we are solving for a range of numbers, not just one.  Let's look at some examples of inequalities
  • 6. Inequalities Look at, and think about, the following signs: The problem is, none of these signs say what they're really supposed to say. Not only that, they are all incorrect. To be correct, they needed to include an inequality.
  • 7. Inequalities Let's put this sign in mathematical terms: Let h = the height required to use the ride. The sign says you must be 46" tall, therefore h = 46" According to the sign, if you're not 46" tall, you cannot ride. But how many people are exactly 46" tall? What they really meant to say was... You must be at least 46" tall, or in mathematical terms... Your height must be equal to or greater than 46". This is our inequality. Our solution is not a single number, but a range of numbers.
  • 8. Inequalities This sign obviously refers to the drinking age. But the sign states that even 22 year olds, or 75 year old people cannot enter. The two words missing here are: at least In mathematical terms, the drinking age is: Equal to or greater than 21 d > 21
  • 9. Inequalities As far as the signs are written: Incorrect Correct
  • 11. Solving Inequalities The process of solving Inequalities is the same as equations except for one rule(which we'll get to later), and how inequalities are shown graphically. Less Than; shown with an open circle on number line; x < -4 Less Than or equal to; shown with closed circle on number line; x < -4
  • 12. Solving Inequalities Greater Than; shown with an open circle on number line; x > -4 Greater Than or equal to; shown with a closed circle on number line; x < -4
  • 13. Solving Inequalities Basic Inequalities 1. Write the inequality shown below x<3 x>0 -5 < x < 2
  • 14. Inequalities Graphing Inequalities Draw a number line and graph the following: 1. 1 <x < 8 2, -2 < x < -1 3. -5 < x <2
  • 15. Solving Inequalities Solve for x and Graph 1. 6x - 7 < 5 1. x < 2; Graph 2. 4(x - 2) > 20 x>3 3. x - 8 < - 6 x<2 And now the one difference between equations & inequalities: Solve for x and Graph 4. -2x < 4; When multiplying or dividing by a negative coefficient, you must switch the sign 4. -2x < 4; -2x/-2 > 4/-2; x > -2
  • 16. Inequalities Think about the rule for example 4 with numbers in there, instead of variables. -2 < 4 You know that the number four is larger than the number negative two: 4 > -2. Multiplying through this inequality by –1, we get –4 < – 2, which the number line shows is true: If we hadn't flipped the inequality, we would have ended up with "–4 > –2", which clearly isn't true. When multiplying or dividing a negative coefficient, you must flip the sign for the inequality to remain true.
  • 17. Solving Inequalities Last 2 Practice Problems; Solve & Graph on Number Line 5. x - 12 < -6 5. x - 12 < -6; +12 +12 6. 6 - 2x > - x +2x +2x 6 > x; x < 6 6. 6 - 2x > - x 5. x < 6;