SlideShare a Scribd company logo
Ch-6 
Linear Inequalities 
Submitted by-Lucky Choudhary 
Submitted To – Mr. N.K Rai Sir 
Date – 8th Sept. 2014
YYEESS WWee CCaann !!!! aallwwaayyss ttrraannssllaattee aa ssttaatteemmeenntt 
pprroobblleemm iinn tthhee ffoorrmm ooff aann eeqquuaattiioonn 
By Using IInneeqquuaalliittiieess ??? 
• i.e., using equations which have the following 
signs between L.H.S And R.H.S 
• For eg :- 40x + 20y ≥ 120
ProPerties of inequalities. 
 Essentially, all of the properties that you learned 
to solve linear equations apply to solving linear 
inequalities with the exception that if you 
multiply or divide by a negative you must 
reverse the inequality sign. 
 So to solve an inequality just do the same steps 
as with an equality to get the variable alone but if 
in the process you multiply or divide by a negative 
let it ring an alarm in your brain that says "Oh 
yeah, I have to turn the sign the other way to 
keep it true".
2x - 6 < 4x + 8 
- 4x - 4x 
- 2x - 6 < 8 
Example 
: 
+ 6 +6 
- 2x <14 
-2 -2 
Ring the alarm! We 
divided by a 
negative! 
We turned the sign! x > -7
Types of inequalities 
STRICT 
• TThhee iinneeqqaalliittiieess wwiitthh << oorr >> 
bbeettwweeeenn tthhee LL..HH..SS && RR..HH..SS 
SLACK 
• TThhee iinneeqqaalliittiieess wwiitthh ≤≤,, oorr ≥≥ 
bbeettwweeeenn tthhee LL..HH..SS && RR..HH..SS 
LINEAR QUADRATIC 
• TThhee iinneeqqaalliittiieess hhaavviinngg tthhee 
ddeeggrreeee 11 
EEgg ::-- 55xx ++22yy >> 1100 
• TThhee iinneeqqaalliittiieess hhaavviinngg tthhee 
ddeeggrreeee 22 
EEgg ::-- 55xx^^22 ++22yy >> 1100
RRuulleess FFoorr SSoollvviinngg IInneeqquuaalliittiieess
Solving Linear Inequalities On A Number Line 
Q1 » » Solve and Show solution on Number LLiinnee 77xx ++33 << 55xx ++99 
Sol » » 77xx –– 55xx << 99 –– 33 » 22xx << 66 » xx << 33 
-5 -4 -3 -2 -1 0 1 2 3 4 5 
PPooiinntt ttoo nnoottee :: -- IIff tthhee eeqquuaalliittyy hhaadd bbeeeenn 77xx ++33 ≤≤ 55xx ++99 tthhee tthhee 
nnuummbbeerr lliinnee wwoouulldd hhaadd bbeeeenn lliikkee tthhiiss 
-5 -4 -3 -2 -1 0 1 2 3 4 5 
IItt iiss iimmppoorrttaanntt ttoo nnoottiiccee tthhee ooppeenn oorr cclloosseedd iinntteerrvvaall ,, wwhhiicchh hhaass ttoo bbee 
uusseedd aaccccoorrddiinngg ttoo tthhee ssiiggnn bbeettwweeeenn tthhee iinneeqquuaalliittyy 
WWhhaatt aabboouutt ssoollvviinngg tthhiiss oonnee 
22 ≤≤ 33xx –– 44 ≤≤ 55 
View Here
QQ11 » » SSoollvvee aanndd SShhooww ssoolluuttiioonn oonn NNuummbbeerr LLiinnee 22 ≤≤ 33xx –– 44 ≤≤ 55 
SSooll » » 
22 ≤≤ 33xx –– 44 ≤≤ 55 » 22 ++ 4 ≤≤ .. 33 x ≤≤ 5 ++ 4 » 
» 66 ≤≤ 33xx ≤≤ 99 » 22 ≤≤ xx ≤≤ 33 
--55 --44 --33 --22 --11 00 11 22 33 44 55 
CClloosseedd IInntteerrvvaall (( )) 
OOppeenn IInntteerrvvaall (( )) 
22..00 22..11 22..22 22..33 22..44 22..55 22..66 22..77 22..88 22..99 33..00
Introduction To Types Of Graphs 
I 
II 
X - Axis 
Y - Axis 
Left half 
plane 
Right half 
plane 
OO 
X - Axis 
Y - Axis 
Upper half 
plane 
Lower half 
plane 
OO
QQss.. » SSoollvvee GGrraapphhiiccaallllyy xx ++yy << 55 X 0 5 
Y 5 0 
SSooll.. » SStteeppss ttoo ssoollvviinngg aanndd ggrraapphhiinngg tthhee IInneeqquuaalliittyy 
Step 1 :- Assume that X + Y = 5 and find the following values 
Step 2 :- Plot these points on graph 
Step 3 :- Choose the half by taking some value for X or Y. if it satisfies the 
inequality then shade that region as the Answer and if doesn’t then the other 
graph is the solution 
Graph of Equation x + y = 5 
If the inequality has ≤ or ≥ 
sign then the the line of 
equation is also the part of 
the graph otherwise it isn’t 
GGrraapphh ooff GGiivveenn IInneeqquuaalliittyy
QQss.. » SSoollvvee GGrraapphhiiccaallllyy xx ++yy << 55 ,, xx >> 33 
X 0 5 
Y 5 0 
SSooll.. » SStteeppss ttoo ssoollvviinngg aanndd ggrraapphhiinngg tthhee IInneeqquuaalliittyy 
Step 1 :- Assume that X + Y = 5 and find the following values 
Step 2 :- Plot these points on graph 
Step 3 :- Choose the half by taking some value for X or Y. if it satisfies the 
inequality then shade that region as the Answer and if doesn’t then the other 
graph is the solution 
Step 4 : - For x > 3 , if we follow the above 
3 steps we get the graphs (green colour) 
And the solution of the given question 
will be the part of the graph common 
to both the inequalities. (Dark Green Colour) 
Graph of Equation x + y = 5 
0 
6 
5 
4 
3 
2 
1 
-2 -1 1 2 33 4 5 6 
-1 
Graph of Equation x = 3
 Hope All Of You Like the 
Presentation 
Thank You

More Related Content

What's hot

Linear equtions with one variable
Linear equtions with one variableLinear equtions with one variable
Linear equtions with one variable
ANKIT SAHOO
 
Linear equations in two variables
Linear equations in two variablesLinear equations in two variables
Linear equations in two variables
Vinisha Pathak
 
Inequalities ppt revised
Inequalities ppt revisedInequalities ppt revised
Inequalities ppt revisedtroxellm
 
IX polynomial
IX polynomialIX polynomial
IX polynomial
Bhawna Khurana
 
Class XI CH 2 (relations and functions)
Class XI CH 2 (relations and functions)Class XI CH 2 (relations and functions)
Class XI CH 2 (relations and functions)
Pradeep Sharma
 
PAIR OF LINEAR EQUATION IN TWO VARIABLE
PAIR OF LINEAR EQUATION IN TWO VARIABLEPAIR OF LINEAR EQUATION IN TWO VARIABLE
PAIR OF LINEAR EQUATION IN TWO VARIABLE
Naveen R
 
PROJECT (PPT) ON PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - CLASS 10
PROJECT (PPT) ON PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - CLASS 10PROJECT (PPT) ON PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - CLASS 10
PROJECT (PPT) ON PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - CLASS 10
mayank78610
 
LINEAR EQUATION IN TWO VARIABLES
LINEAR EQUATION IN TWO VARIABLESLINEAR EQUATION IN TWO VARIABLES
LINEAR EQUATION IN TWO VARIABLES
Manah Chhabra
 
Conic Sections (Class 11 Project)
Conic Sections (Class 11 Project)Conic Sections (Class 11 Project)
Conic Sections (Class 11 Project)
KushagraAgrawal46
 
Matrices & Determinants
Matrices & DeterminantsMatrices & Determinants
Matrices & Determinants
Birinder Singh Gulati
 
Real numbers- class 10 mathematics
Real numbers- class 10 mathematicsReal numbers- class 10 mathematics
Real numbers- class 10 mathematics
Amit Choube
 
Algebraic expressions and identities
Algebraic expressions and identitiesAlgebraic expressions and identities
Algebraic expressions and identities
Deepansha Singh
 
CLASS IX MATHS Coordinate geometry ppt
CLASS IX MATHS Coordinate geometry pptCLASS IX MATHS Coordinate geometry ppt
CLASS IX MATHS Coordinate geometry ppt
Rc Os
 
Straight Lines ( Especially For XI )
Straight Lines ( Especially For XI ) Straight Lines ( Especially For XI )
Straight Lines ( Especially For XI )
Atit Gaonkar
 
class 10 chapter 1- real numbers
class 10 chapter 1- real numbersclass 10 chapter 1- real numbers
class 10 chapter 1- real numbers
karan saini
 
Mathematics class XI SETS
Mathematics class XI SETSMathematics class XI SETS
Mathematics class XI SETS
Naveen R
 
Class9 number system
Class9  number systemClass9  number system
Class9 number system
Shija John
 
Maths ppt linear equations in two variables
Maths ppt   linear equations in two variablesMaths ppt   linear equations in two variables
Maths ppt linear equations in two variables
gobilladraksharani
 
Absolute Value Inequalities
Absolute Value InequalitiesAbsolute Value Inequalities
Absolute Value Inequalitiesswartzje
 
Maths Project 11 class(SETS)
Maths Project 11 class(SETS)Maths Project 11 class(SETS)
Maths Project 11 class(SETS)
Sahil Mehra
 

What's hot (20)

Linear equtions with one variable
Linear equtions with one variableLinear equtions with one variable
Linear equtions with one variable
 
Linear equations in two variables
Linear equations in two variablesLinear equations in two variables
Linear equations in two variables
 
Inequalities ppt revised
Inequalities ppt revisedInequalities ppt revised
Inequalities ppt revised
 
IX polynomial
IX polynomialIX polynomial
IX polynomial
 
Class XI CH 2 (relations and functions)
Class XI CH 2 (relations and functions)Class XI CH 2 (relations and functions)
Class XI CH 2 (relations and functions)
 
PAIR OF LINEAR EQUATION IN TWO VARIABLE
PAIR OF LINEAR EQUATION IN TWO VARIABLEPAIR OF LINEAR EQUATION IN TWO VARIABLE
PAIR OF LINEAR EQUATION IN TWO VARIABLE
 
PROJECT (PPT) ON PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - CLASS 10
PROJECT (PPT) ON PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - CLASS 10PROJECT (PPT) ON PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - CLASS 10
PROJECT (PPT) ON PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - CLASS 10
 
LINEAR EQUATION IN TWO VARIABLES
LINEAR EQUATION IN TWO VARIABLESLINEAR EQUATION IN TWO VARIABLES
LINEAR EQUATION IN TWO VARIABLES
 
Conic Sections (Class 11 Project)
Conic Sections (Class 11 Project)Conic Sections (Class 11 Project)
Conic Sections (Class 11 Project)
 
Matrices & Determinants
Matrices & DeterminantsMatrices & Determinants
Matrices & Determinants
 
Real numbers- class 10 mathematics
Real numbers- class 10 mathematicsReal numbers- class 10 mathematics
Real numbers- class 10 mathematics
 
Algebraic expressions and identities
Algebraic expressions and identitiesAlgebraic expressions and identities
Algebraic expressions and identities
 
CLASS IX MATHS Coordinate geometry ppt
CLASS IX MATHS Coordinate geometry pptCLASS IX MATHS Coordinate geometry ppt
CLASS IX MATHS Coordinate geometry ppt
 
Straight Lines ( Especially For XI )
Straight Lines ( Especially For XI ) Straight Lines ( Especially For XI )
Straight Lines ( Especially For XI )
 
class 10 chapter 1- real numbers
class 10 chapter 1- real numbersclass 10 chapter 1- real numbers
class 10 chapter 1- real numbers
 
Mathematics class XI SETS
Mathematics class XI SETSMathematics class XI SETS
Mathematics class XI SETS
 
Class9 number system
Class9  number systemClass9  number system
Class9 number system
 
Maths ppt linear equations in two variables
Maths ppt   linear equations in two variablesMaths ppt   linear equations in two variables
Maths ppt linear equations in two variables
 
Absolute Value Inequalities
Absolute Value InequalitiesAbsolute Value Inequalities
Absolute Value Inequalities
 
Maths Project 11 class(SETS)
Maths Project 11 class(SETS)Maths Project 11 class(SETS)
Maths Project 11 class(SETS)
 

Similar to Ch- 6 Linear inequalities of class 11

Solving Systems of Linear Inequalities
Solving Systems of Linear InequalitiesSolving Systems of Linear Inequalities
Solving Systems of Linear Inequalitiesswartzje
 
matrices and algbra
matrices and algbramatrices and algbra
matrices and algbra
gandhinagar
 
Chapter 1 Functions
Chapter 1 FunctionsChapter 1 Functions
Chapter 1 Functions
Jenny Hubbard
 
6.7 quadratic inequalities
6.7 quadratic inequalities6.7 quadratic inequalities
6.7 quadratic inequalitiesJessica Garcia
 
System of linear inequalities
System of linear inequalitiesSystem of linear inequalities
System of linear inequalitiesmstf mstf
 
Applied numerical methods lec6
Applied numerical methods lec6Applied numerical methods lec6
Applied numerical methods lec6
Yasser Ahmed
 
01_SLR_final (1).pptx
01_SLR_final (1).pptx01_SLR_final (1).pptx
01_SLR_final (1).pptx
DR. MAQSOOD AHMAD
 
Gauss Jordan
Gauss JordanGauss Jordan
Gauss Jordan
Ezzat Gul
 
15 regression basics
15 regression basics15 regression basics
15 regression basicsgaurav arora
 
Reliable multimedia transmission under noisy condition
Reliable multimedia transmission under noisy conditionReliable multimedia transmission under noisy condition
Reliable multimedia transmission under noisy condition
Shahrukh Ali Khan
 
Interpolation and Extrapolation
Interpolation and ExtrapolationInterpolation and Extrapolation
Interpolation and Extrapolation
VNRacademy
 
Solving quadratic equations
Solving quadratic equationsSolving quadratic equations
Solving quadratic equationsAsawari Warkad
 
Power series
Power series Power series
Power series
Pranav Veerani
 
System of linear equation and matrices
System of linear equation and matricesSystem of linear equation and matrices
System of linear equation and matrices
Adani Institute of Infrastructure Engineering College
 
Condition (linear algebra)
Condition (linear algebra)Condition (linear algebra)
UNIT I_5.pdf
UNIT I_5.pdfUNIT I_5.pdf
UNIT I_5.pdf
Muthukumar P
 

Similar to Ch- 6 Linear inequalities of class 11 (20)

Solving Systems of Linear Inequalities
Solving Systems of Linear InequalitiesSolving Systems of Linear Inequalities
Solving Systems of Linear Inequalities
 
0
00
0
 
matrices and algbra
matrices and algbramatrices and algbra
matrices and algbra
 
Chapter 1 Functions
Chapter 1 FunctionsChapter 1 Functions
Chapter 1 Functions
 
6.7 quadratic inequalities
6.7 quadratic inequalities6.7 quadratic inequalities
6.7 quadratic inequalities
 
System of linear inequalities
System of linear inequalitiesSystem of linear inequalities
System of linear inequalities
 
Applied numerical methods lec6
Applied numerical methods lec6Applied numerical methods lec6
Applied numerical methods lec6
 
01_SLR_final (1).pptx
01_SLR_final (1).pptx01_SLR_final (1).pptx
01_SLR_final (1).pptx
 
Gauss Jordan
Gauss JordanGauss Jordan
Gauss Jordan
 
1
11
1
 
15 regression basics
15 regression basics15 regression basics
15 regression basics
 
Reliable multimedia transmission under noisy condition
Reliable multimedia transmission under noisy conditionReliable multimedia transmission under noisy condition
Reliable multimedia transmission under noisy condition
 
Interpolation and Extrapolation
Interpolation and ExtrapolationInterpolation and Extrapolation
Interpolation and Extrapolation
 
Solving quadratic equations
Solving quadratic equationsSolving quadratic equations
Solving quadratic equations
 
Systems of linear equations; matrices
Systems of linear equations; matricesSystems of linear equations; matrices
Systems of linear equations; matrices
 
Computational Dynamics edited
Computational Dynamics editedComputational Dynamics edited
Computational Dynamics edited
 
Power series
Power series Power series
Power series
 
System of linear equation and matrices
System of linear equation and matricesSystem of linear equation and matrices
System of linear equation and matrices
 
Condition (linear algebra)
Condition (linear algebra)Condition (linear algebra)
Condition (linear algebra)
 
UNIT I_5.pdf
UNIT I_5.pdfUNIT I_5.pdf
UNIT I_5.pdf
 

Recently uploaded

Guidance_and_Counselling.pdf B.Ed. 4th Semester
Guidance_and_Counselling.pdf B.Ed. 4th SemesterGuidance_and_Counselling.pdf B.Ed. 4th Semester
Guidance_and_Counselling.pdf B.Ed. 4th Semester
Atul Kumar Singh
 
Model Attribute Check Company Auto Property
Model Attribute  Check Company Auto PropertyModel Attribute  Check Company Auto Property
Model Attribute Check Company Auto Property
Celine George
 
special B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdfspecial B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdf
Special education needs
 
Polish students' mobility in the Czech Republic
Polish students' mobility in the Czech RepublicPolish students' mobility in the Czech Republic
Polish students' mobility in the Czech Republic
Anna Sz.
 
CLASS 11 CBSE B.St Project AIDS TO TRADE - INSURANCE
CLASS 11 CBSE B.St Project AIDS TO TRADE - INSURANCECLASS 11 CBSE B.St Project AIDS TO TRADE - INSURANCE
CLASS 11 CBSE B.St Project AIDS TO TRADE - INSURANCE
BhavyaRajput3
 
Lapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdfLapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdf
Jean Carlos Nunes Paixão
 
Instructions for Submissions thorugh G- Classroom.pptx
Instructions for Submissions thorugh G- Classroom.pptxInstructions for Submissions thorugh G- Classroom.pptx
Instructions for Submissions thorugh G- Classroom.pptx
Jheel Barad
 
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdfAdversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
Po-Chuan Chen
 
Unit 2- Research Aptitude (UGC NET Paper I).pdf
Unit 2- Research Aptitude (UGC NET Paper I).pdfUnit 2- Research Aptitude (UGC NET Paper I).pdf
Unit 2- Research Aptitude (UGC NET Paper I).pdf
Thiyagu K
 
Chapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptxChapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptx
Mohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
 
2024.06.01 Introducing a competency framework for languag learning materials ...
2024.06.01 Introducing a competency framework for languag learning materials ...2024.06.01 Introducing a competency framework for languag learning materials ...
2024.06.01 Introducing a competency framework for languag learning materials ...
Sandy Millin
 
Home assignment II on Spectroscopy 2024 Answers.pdf
Home assignment II on Spectroscopy 2024 Answers.pdfHome assignment II on Spectroscopy 2024 Answers.pdf
Home assignment II on Spectroscopy 2024 Answers.pdf
Tamralipta Mahavidyalaya
 
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
Levi Shapiro
 
Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345
beazzy04
 
Acetabularia Information For Class 9 .docx
Acetabularia Information For Class 9  .docxAcetabularia Information For Class 9  .docx
Acetabularia Information For Class 9 .docx
vaibhavrinwa19
 
Digital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and ResearchDigital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and Research
Vikramjit Singh
 
Palestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptxPalestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptx
RaedMohamed3
 
The geography of Taylor Swift - some ideas
The geography of Taylor Swift - some ideasThe geography of Taylor Swift - some ideas
The geography of Taylor Swift - some ideas
GeoBlogs
 
678020731-Sumas-y-Restas-Para-Colorear.pdf
678020731-Sumas-y-Restas-Para-Colorear.pdf678020731-Sumas-y-Restas-Para-Colorear.pdf
678020731-Sumas-y-Restas-Para-Colorear.pdf
CarlosHernanMontoyab2
 
Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.
Ashokrao Mane college of Pharmacy Peth-Vadgaon
 

Recently uploaded (20)

Guidance_and_Counselling.pdf B.Ed. 4th Semester
Guidance_and_Counselling.pdf B.Ed. 4th SemesterGuidance_and_Counselling.pdf B.Ed. 4th Semester
Guidance_and_Counselling.pdf B.Ed. 4th Semester
 
Model Attribute Check Company Auto Property
Model Attribute  Check Company Auto PropertyModel Attribute  Check Company Auto Property
Model Attribute Check Company Auto Property
 
special B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdfspecial B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdf
 
Polish students' mobility in the Czech Republic
Polish students' mobility in the Czech RepublicPolish students' mobility in the Czech Republic
Polish students' mobility in the Czech Republic
 
CLASS 11 CBSE B.St Project AIDS TO TRADE - INSURANCE
CLASS 11 CBSE B.St Project AIDS TO TRADE - INSURANCECLASS 11 CBSE B.St Project AIDS TO TRADE - INSURANCE
CLASS 11 CBSE B.St Project AIDS TO TRADE - INSURANCE
 
Lapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdfLapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdf
 
Instructions for Submissions thorugh G- Classroom.pptx
Instructions for Submissions thorugh G- Classroom.pptxInstructions for Submissions thorugh G- Classroom.pptx
Instructions for Submissions thorugh G- Classroom.pptx
 
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdfAdversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
 
Unit 2- Research Aptitude (UGC NET Paper I).pdf
Unit 2- Research Aptitude (UGC NET Paper I).pdfUnit 2- Research Aptitude (UGC NET Paper I).pdf
Unit 2- Research Aptitude (UGC NET Paper I).pdf
 
Chapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptxChapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptx
 
2024.06.01 Introducing a competency framework for languag learning materials ...
2024.06.01 Introducing a competency framework for languag learning materials ...2024.06.01 Introducing a competency framework for languag learning materials ...
2024.06.01 Introducing a competency framework for languag learning materials ...
 
Home assignment II on Spectroscopy 2024 Answers.pdf
Home assignment II on Spectroscopy 2024 Answers.pdfHome assignment II on Spectroscopy 2024 Answers.pdf
Home assignment II on Spectroscopy 2024 Answers.pdf
 
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
 
Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345
 
Acetabularia Information For Class 9 .docx
Acetabularia Information For Class 9  .docxAcetabularia Information For Class 9  .docx
Acetabularia Information For Class 9 .docx
 
Digital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and ResearchDigital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and Research
 
Palestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptxPalestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptx
 
The geography of Taylor Swift - some ideas
The geography of Taylor Swift - some ideasThe geography of Taylor Swift - some ideas
The geography of Taylor Swift - some ideas
 
678020731-Sumas-y-Restas-Para-Colorear.pdf
678020731-Sumas-y-Restas-Para-Colorear.pdf678020731-Sumas-y-Restas-Para-Colorear.pdf
678020731-Sumas-y-Restas-Para-Colorear.pdf
 
Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.
 

Ch- 6 Linear inequalities of class 11

  • 1. Ch-6 Linear Inequalities Submitted by-Lucky Choudhary Submitted To – Mr. N.K Rai Sir Date – 8th Sept. 2014
  • 2.
  • 3. YYEESS WWee CCaann !!!! aallwwaayyss ttrraannssllaattee aa ssttaatteemmeenntt pprroobblleemm iinn tthhee ffoorrmm ooff aann eeqquuaattiioonn By Using IInneeqquuaalliittiieess ??? • i.e., using equations which have the following signs between L.H.S And R.H.S • For eg :- 40x + 20y ≥ 120
  • 4. ProPerties of inequalities.  Essentially, all of the properties that you learned to solve linear equations apply to solving linear inequalities with the exception that if you multiply or divide by a negative you must reverse the inequality sign.  So to solve an inequality just do the same steps as with an equality to get the variable alone but if in the process you multiply or divide by a negative let it ring an alarm in your brain that says "Oh yeah, I have to turn the sign the other way to keep it true".
  • 5. 2x - 6 < 4x + 8 - 4x - 4x - 2x - 6 < 8 Example : + 6 +6 - 2x <14 -2 -2 Ring the alarm! We divided by a negative! We turned the sign! x > -7
  • 6. Types of inequalities STRICT • TThhee iinneeqqaalliittiieess wwiitthh << oorr >> bbeettwweeeenn tthhee LL..HH..SS && RR..HH..SS SLACK • TThhee iinneeqqaalliittiieess wwiitthh ≤≤,, oorr ≥≥ bbeettwweeeenn tthhee LL..HH..SS && RR..HH..SS LINEAR QUADRATIC • TThhee iinneeqqaalliittiieess hhaavviinngg tthhee ddeeggrreeee 11 EEgg ::-- 55xx ++22yy >> 1100 • TThhee iinneeqqaalliittiieess hhaavviinngg tthhee ddeeggrreeee 22 EEgg ::-- 55xx^^22 ++22yy >> 1100
  • 7. RRuulleess FFoorr SSoollvviinngg IInneeqquuaalliittiieess
  • 8. Solving Linear Inequalities On A Number Line Q1 » » Solve and Show solution on Number LLiinnee 77xx ++33 << 55xx ++99 Sol » » 77xx –– 55xx << 99 –– 33 » 22xx << 66 » xx << 33 -5 -4 -3 -2 -1 0 1 2 3 4 5 PPooiinntt ttoo nnoottee :: -- IIff tthhee eeqquuaalliittyy hhaadd bbeeeenn 77xx ++33 ≤≤ 55xx ++99 tthhee tthhee nnuummbbeerr lliinnee wwoouulldd hhaadd bbeeeenn lliikkee tthhiiss -5 -4 -3 -2 -1 0 1 2 3 4 5 IItt iiss iimmppoorrttaanntt ttoo nnoottiiccee tthhee ooppeenn oorr cclloosseedd iinntteerrvvaall ,, wwhhiicchh hhaass ttoo bbee uusseedd aaccccoorrddiinngg ttoo tthhee ssiiggnn bbeettwweeeenn tthhee iinneeqquuaalliittyy WWhhaatt aabboouutt ssoollvviinngg tthhiiss oonnee 22 ≤≤ 33xx –– 44 ≤≤ 55 View Here
  • 9. QQ11 » » SSoollvvee aanndd SShhooww ssoolluuttiioonn oonn NNuummbbeerr LLiinnee 22 ≤≤ 33xx –– 44 ≤≤ 55 SSooll » » 22 ≤≤ 33xx –– 44 ≤≤ 55 » 22 ++ 4 ≤≤ .. 33 x ≤≤ 5 ++ 4 » » 66 ≤≤ 33xx ≤≤ 99 » 22 ≤≤ xx ≤≤ 33 --55 --44 --33 --22 --11 00 11 22 33 44 55 CClloosseedd IInntteerrvvaall (( )) OOppeenn IInntteerrvvaall (( )) 22..00 22..11 22..22 22..33 22..44 22..55 22..66 22..77 22..88 22..99 33..00
  • 10.
  • 11. Introduction To Types Of Graphs I II X - Axis Y - Axis Left half plane Right half plane OO X - Axis Y - Axis Upper half plane Lower half plane OO
  • 12. QQss.. » SSoollvvee GGrraapphhiiccaallllyy xx ++yy << 55 X 0 5 Y 5 0 SSooll.. » SStteeppss ttoo ssoollvviinngg aanndd ggrraapphhiinngg tthhee IInneeqquuaalliittyy Step 1 :- Assume that X + Y = 5 and find the following values Step 2 :- Plot these points on graph Step 3 :- Choose the half by taking some value for X or Y. if it satisfies the inequality then shade that region as the Answer and if doesn’t then the other graph is the solution Graph of Equation x + y = 5 If the inequality has ≤ or ≥ sign then the the line of equation is also the part of the graph otherwise it isn’t GGrraapphh ooff GGiivveenn IInneeqquuaalliittyy
  • 13. QQss.. » SSoollvvee GGrraapphhiiccaallllyy xx ++yy << 55 ,, xx >> 33 X 0 5 Y 5 0 SSooll.. » SStteeppss ttoo ssoollvviinngg aanndd ggrraapphhiinngg tthhee IInneeqquuaalliittyy Step 1 :- Assume that X + Y = 5 and find the following values Step 2 :- Plot these points on graph Step 3 :- Choose the half by taking some value for X or Y. if it satisfies the inequality then shade that region as the Answer and if doesn’t then the other graph is the solution Step 4 : - For x > 3 , if we follow the above 3 steps we get the graphs (green colour) And the solution of the given question will be the part of the graph common to both the inequalities. (Dark Green Colour) Graph of Equation x + y = 5 0 6 5 4 3 2 1 -2 -1 1 2 33 4 5 6 -1 Graph of Equation x = 3
  • 14.  Hope All Of You Like the Presentation Thank You