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Question (1):
What is a solution set?
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Answer:
The subset of the replacement set which satisfies the values of the variable is called the solution set.
Example:
Solution set= {1}
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Question (2):
Represent the following inequalities on real number lines:
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Answer:
a) 2x-1<3
2x<4
i.e., x<2
b) 3x+1 -5
3x -6
x -2
d) -2  x<3
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Question (3):
Represent 2x-1<5 on the number line.
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Answer:
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Question (4):
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Answer:
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Question (5):
Solve the inequation  and graph the solution set on the number line.
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Answer:
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Question (6):
Represent the solution of the following inequalities on a real number line.
a) 
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Answer:
a) 
 (multiplying both sides by negative sign)
When both sides are multiplied by negative sign, the inequality is reversed.
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Question (7):
Draw the graph of the solution set of the following systems of Inequation
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Answer:
The lines corresponding to 4x + 5y = 20, and 3x + 4y = 24 are shown in the graph.
Consider the origin (0, 0). This point satisfies the inequality 
Therefore the closed half plane containing (0, 0) is the graph of 
On the other hand, the point (0, 0) does not satisfy the inequation 
Therefore the closed half plane, not containing (0, 0) is the graph of this inequation.
Since the intersection of these half planes is empty. The solution set is empty.
 
The line corresponding (1) is x + 2y = 4
Consider the point (0, 0). Let us find if the point satisfies inequation (1),
 is not true
Therefore (0, 0) does not line in the closed half plane 
Therefore the closed half plane not containing (0, 0) is the graph of (1).
Similarly, the closed figure not containing (0, 0) is the graph of (2).
The solution set is empty.
The lines corresponding to (1), (2) and (3) are shown in the graph. The closed half planes corresponding to (1) and (2) and (3) are shaded.
The intersection of these half planes is the interior and boundary of 
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Question (8):
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Answer:
This is true if either
No value of x satisfies (i). Thus (i) gives no solution.
Graphical representation
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Question (9):
Find the solution set of the inequation 3-8x-3x2 0 and represent the solution set on the number line.
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Answer:
The given equation is
 
 
 
This is true if either
i.e., if either
(ii) is not true and gives no solution.
Graphical representation
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Question (10):
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Answer:
 
 
This is true if either
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Question (11):
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Answer:
 
 
 
This is true if either
No value of x satisfies (ii). Thus, (ii) gives no solution.
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Question (12):
Exhibit graphically the solution sets of the following linear inequations.
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Answer:
We draw the graph of 2x + 3y = 6 by taking the points A(0, 2) and B(3, 0).
The line divides the region into two, parts I and II.
(0, 0) satisfies the inequation 2x + 3y  6.
 I is the required region.
Step I:
We draw the lines
x + y = 3 ...(i)
x + 2y = 4 ...(ii)
x = 0 ...(iii)
y = 0 ...(iv)
(i) and (ii) can be written as
Now (i) passes through the points A(3,0) and B(0,3) and (ii) passes through the points C(4,0) and D(0,2).
Solving (i) and (ii), we get
Therefore, the coordinates of point E are (2,1).
Step II:
We shade the region satisfied by
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