The document discusses inequalities and their solutions. It defines strict and slack inequalities using symbols like <, >, ≤, and ≥. Examples of linear inequalities are given and it is explained that the number line can be used to show the solution set, with open and closed intervals depending on the inequality symbols. The rules for solving linear inequalities on a number line are presented. Types of graphs are introduced, including using graphs to solve systems of inequalities by plotting points that satisfy both inequalities and shading the common region.

3. YES We Can !!YES We Can !! always translate a statementalways translate a statement
problem in the form of an equationproblem in the form of an equation
By Using InequalitiesInequalities ???
• i.e., using equations which have the following
signs between L.H.S And R.H.S
• For eg :- 40x + 20y ≥ 120

4. YES We Can !!YES We Can !! always translate a statementalways translate a statement
problem in the form of an equationproblem in the form of an equation
By Using InequalitiesInequalities ???
• i.e., using equations which have the following
signs between L.H.S And R.H.S
• For eg :- 40x + 20y ≤ 120

5. YES We Can !!YES We Can !! always translate a statementalways translate a statement
problem in the form of an equationproblem in the form of an equation
By Using InequalitiesInequalities ???
• i.e., using equations which have the following
signs between L.H.S And R.H.S
• For eg :- 40x + 20y < 120

6. YES We Can !!YES We Can !! always translate a statementalways translate a statement
problem in the form of an equationproblem in the form of an equation
By Using InequalitiesInequalities ???
• i.e., using equations which have the following
signs between L.H.S And R.H.S
• For eg :- 40x + 20y > 120

7. Types of inequalities
STRICT
• 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 theThe ineqalities having the
degree 1degree 1
Eg :- 5x +2y > 10Eg :- 5x +2y > 10
• The ineqalities having theThe ineqalities having the
degree 2degree 2
Eg :- 5x^2 +2y > 10Eg :- 5x^2 +2y > 10
LINEAR QUADRATIC

8. Rules For Solving InequalitiesRules For Solving Inequalities

9. Solving Linear Inequalities On A Number Line
Q1 » » Solve and Show solution on Number Line 7x +3 < 5x +9Solve 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 theIf 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 beIt 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 inequality
What about solving this oneWhat 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 ≤ 52 ≤ 3x – 4 ≤ 5
View Here

10. 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 3.02.0 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 ( )

12. 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

13. 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 < 5Solve 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

14. 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 common
to both the inequalities. (Dark Green Colour)
Qs. »Qs. » Solve Graphically x +y < 5 , x > 3Solve 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 21 433 5 6
Graph of Equation x = 3