Linear Inequality Chapter 6 Class XI : Basics
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Case III
Case IV
Case V
 A point in the Cartesian plane either lie on the line or lie on either of the half plane.
 The region containing all the solutions of an inequality is called the solution region or feasible region.
 In order to identify the half plane represented by an inequality, it is sufficient to take any point (a, b) (not on the line ) and check whether it satisfies the inequality or not.
 If it satisfies the given inequality then the half plane in which the point lie is called the solution region.
 If the point does not satisfy the inequality then the region in which the point does not lie is called the solution region. For convenience the point (0,0) is preferred.
 We should shade the solution region identified in the above steps.
 For the inequality with the sign ≤ or ≥ , the points on the line are also included in the solution region or feasible region. In this case the graph line is the full line.
 For the inequality with the sign < or >, the points on the line are not included in the feasible region or solution region. In this case the graph line is a dotted line as shown in the figure.
 Here we may be given two or three or four equations.
 We find the solution region for all the equations as discussed above.
 The common solution region of all the equations in the given system is called the solution region or feasible region of the system of equations.
Case I \[2560+4x\leq 5120+2x\] \[4x2x\leq 51202560\] \[2x\leq 2560\] \[x\leq 1280\] 
Case II \[5120+2x\leq 3840+6x\] \[51203840\leq 6x2x\] \[1280\leq 4x\] \[1280\leq 4x\] \[320\leq x\] 
\[320\leq x\leq 1280\]

Case Study Based Questions 
Ans 
1 
Marks obtained by
Radhika in quarterly and half yearly examinations of Mathematics are 60 and
70 respectively. Based on the above
information, answer the following questions 

(i) 
Minimum
marks she should get in the annual exam to have an average of atleast 70
marks is a)
80 b) 85
c) 75
d)
90 
a 
(ii) 
Maximum
marks, she should get in the annual exam to have an average of atmost 75
marks is a)
85 b) 90
c) 95
d) 80 
c 
(iii) 
Range
of marks in annual exam, so that the average marks is atleast 60 and atmost
70 is a)
[60, 70]
b) [50, 80] c) [50, 70] d) [60, 80] 
b 
(iv) 
If
the average of atleast 60 marks is considered pass, then minimum marks she
need to score in annual exam to pass is a)
60 b) 65 c) 70 d) 50 
d 
(v) 
If
she scored atleast 20 and atmost 80 marks in annual exam, then the range of
average marks is a)
[50, 70]
b) [60, 70] c) 50, 60] d [50, 80] 
a 
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