YES We Can !! YES We Can !! always translate a statement always translate a statement problem in the form of an equationproblem in the form of an equationBy Using InequalitiesInequalities ???

• i.e., using equations which have the following signs between L.H.S And R.H.S

• For eg :- 40x + 20y ≥ 120

YES We Can !! YES We Can !! always translate a statement always translate a statement problem in the form of an equationproblem in the form of an equationBy Using InequalitiesInequalities ???

• i.e., using equations which have the following signs between L.H.S And R.H.S

• For eg :- 40x + 20y ≤ 120

YES We Can !! YES We Can !! always translate a statement always translate a statement problem in the form of an equationproblem in the form of an equationBy Using InequalitiesInequalities ???

• i.e., using equations which have the following signs between L.H.S And R.H.S

• For eg :- 40x + 20y < 120

YES We Can !!YES We Can !! always translate a statement always translate a statement problem in the form of an equationproblem in the form of an equationBy Using InequalitiesInequalities ???

• i.e., using equations which have the following signs between L.H.S And R.H.S

• For eg :- 40x + 20y > 120

Types of inequalitiesSTRICT

• The ineqalities with < or > The ineqalities with < or > between the L.H.S & R.H.Sbetween the L.H.S & R.H.S

SLACK

• The ineqalities with ≤, or ≥ The ineqalities with ≤, or ≥ between the L.H.S & R.H.Sbetween the L.H.S & R.H.S

• The ineqalities having the The ineqalities having the degree 1degree 1

Eg :- 5x +2y > 10Eg :- 5x +2y > 10

• The ineqalities having the The ineqalities having the degree 2degree 2 Eg :- 5x^2 +2y > 10Eg :- 5x^2 +2y > 10

LINEAR QUADRATIC

Rules For Solving InequalitiesRules For Solving Inequalities

Solving Linear Inequalities On A Number Line

Q1 » » Solve and Show solution on Number Line 7x +3 < 5x +9 Solve and Show solution on Number Line 7x +3 < 5x +9

Sol » » » » 7x – 5x < 9 – 3 » 2x < 6 » x < 37x – 5x < 9 – 3 » 2x < 6 » x < 3

Point to note : -Point to note : - If the equality had been 7x +3 ≤ 5x +9 the the If the equality had been 7x +3 ≤ 5x +9 the the number line would had been like thisnumber line would had been like this

It is important to notice the open or closed interval , which has to be It is important to notice the open or closed interval , which has to be used according to the sign between the inequalityused according to the sign between the inequalityWhat about solving this one What about solving this one

-5 -4 -3 -2 -1 0 1 2 3 4 5

-5 -4 -3 -2 -1 0 1 2 3 4 5

2 ≤ 3x – 4 ≤ 5 2 ≤ 3x – 4 ≤ 5 View Here

Q1 » » Q1 » » Solve and Show solution on Number Line 2 ≤ 3x – 4 ≤ 5Solve and Show solution on Number Line 2 ≤ 3x – 4 ≤ 5 Sol » » Sol » »

. . 2 ≤ 3x – 4 ≤ 5 » 2 + 4 ≤ 3x ≤ 5 + 4 » 2 ≤ 3x – 4 ≤ 5 » 2 + 4 ≤ 3x ≤ 5 + 4 » » 6 ≤ 3x ≤ 9 » 2 ≤ x ≤ 3 » 6 ≤ 3x ≤ 9 » 2 ≤ x ≤ 3

-5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5

2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0

Closed Interval ( )Closed Interval ( )Open Interval ( )Open Interval ( )

Introduction To Types Of Graphs

I

II

X - Axis

Y - Axis

Left half plane

Right half plane

OO

X - Axis

Y - AxisUpper half

plane

Lower half plane

OO

Sol. » Sol. » Steps to solving and graphing the InequalitySteps to solving and graphing the Inequality

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

Qs. » Qs. » Solve Graphically x +y < 5 Solve Graphically x +y < 5 X 0 5

Y 5 0

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 Graph of Given InequalityGraph of Given Inequality

Sol. » Sol. » Steps to solving and graphing the InequalitySteps to solving and graphing the Inequality

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 commonto both the inequalities. (Dark Green Colour)

Qs. » Qs. » Solve Graphically x +y < 5 , x > 3 Solve Graphically x +y < 5 , x > 3 X 0 5

Y 5 0

Graph of Equation x + y = 5

0

-1

1

2

3

4

5

6

-1 -2 2 1 4 33 5 6Graph of Equation x = 3