Mathematics Lab Activity-11 Class XI

Mathematics Laboratory Activities on Linear Ineqality for class XI students Non-Medical. These activities are strictly according to the CBSE syllabus

Chapter - 5 | Linear Inequality

Activity - 11

Objective

To verify that the graph of a given inequality, say. 5x + 4y – 40 < 0  represent only one of the two half planes.

Material Required

Cardboard, thick white paper, sketch pens , ruler , adhesive.

Theory

Inequality :- Two real numbers or two algebraic expressions related by the symbol ‘<’,  ‘>’ ,   ‘≤’ ,  ‘≥’ are said to form an inequality

Linear inequalities in one variable :-

Inequalities of the type ax + by > 0 or ax + by < 0 are called inequalities in one variable

Linear inequalities in two variable :-

Inequalities of the type ax + by ≤ 0 or ax + by ≥ 0 are called inequalities in two variable.

Procedure

1. Take a cardboard of convenient size and paste a white paper on it .

2. Draw two mutually perpendicular lines X’OX and Y’OX to represent x- axis and y-axis respectively

X	0	8
Y	10	0

3.Find the two points on the line 5x +4y – 40 = 0 and draw its graph as shown in figure 13.1   

Figure 13.1

4. Mark the two half planes as I and II

5. Now take the check point O(0,0) and put these values in the inequality 5x + 4y – 40 < 0 we get

                              5 x 0 + 4 x 0 – 40 < 0

                                                      -40 < 0 , yes it is true

This means that the point O (0, 0) lies in the solution region of the given inequality.

6. Region I is called the solution region or feasible region. If point (0, 0) does not satisfy the above inequality then region II is called the solution region or feasible region.

7. Graph of the inequality of the form  ax + by < 0, where  constant term C = 0, always passes through the origin O(0, 0). In this case (0, 0) cannot be taken as the check point. In this case check point can be taken either (a, 0) or (0, b). 

Observations

1. Any line represented on the Cartesian coordinate plane divide the plane into two half planes, I and II.

2. If any check point from the half plane I satisfy the given inequality then half plane I is called the solution region or feasible region.

3. If any check point from half plane II satisfy the given inequality then half plane II is called the solution region or feasible region.

4. For all the graph lines which do not pass through the origin, (0,0) can be taken as the check point.

5. For all the graph lines which pass through the origin, the points of the form (a,0) or (0,b) can be taken as the check point.

Result

The graph of any  given inequality can represents only one half plane.

Applications

This activity can be used to identify the half plane which provides the solution of a given inequality.

VIVA – VOICE

Q. 1. What is an inequality?

Ans. Two real numbers or two algebraic expressions related by the symbols  <, >, ≤  and ≥ are said to be an inequality.

Q. 2. What do you mean by solutions of an inequality?

Ans. The values of an inequality which make the inequality a true statement, are called the solutions of the inequality.

Q. 3. What do you mean by the feasible region?

Ans. The region containing all the solutions of the given inequality is called solution region or feasible region.

Q. 4. What is the check point?

Ans. It is the point taken from any one of the half plane which make the inequality either true or false.

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