Previously we have discussed about antiderivative of sin2x and In today's session we are going to discuss about Compound Inequalities which comes under board of intermediate education ap, Equations are a combination of two or more variables with the numbers. Solving Absolute Value Equations by using various types of properties and different type of operations is shown here. In this session, we will talk about inequalities, especially Compound Inequalities. An inequality is similar to an equation as we solve the inequality by adding or subtracting the variables from it. The difference is that we use comparison operators (>, <, >=, <=, ≠) rather than equality symbol (=). Here we are going to discuss about the concept of solving Compound Inequalities.
We can define Compound Inequalities as the combination of two or more inequalities bound with the ‘and’ or ‘or’ symbol.
Let’s show you the example of inequalities:
Suppose two inequalities are given:
(a) 5y – 4 < 7
(b) y + 12 > 13
Then both the above inequalities can be represented as Compound Inequalities as:
5y – 4 < 7 and y + 12 > 13
The above representations of inequalities are known as compound inequalities or generally known as conjunction of inequalities.(want to Learn more about Inequalities, click here),
Example2: (a) 5y > 65
(b) m + 7 < 3
The above inequalities can be represented in below given format:
5y > 65 or m + 7 < 3
The above representations of inequalities are known as disjunction of inequalities. Now we show you how to solve the compound inequalities:
Example: Solve the given compound inequalities 5y – 4 < 7 and y + 12 > 13 ?
Solution: Here we solve the inequalities in different way:
=> 5y – 4 < 7
Now we add 4 in both sides
ð 5y – 4 + 4 < 7 + 4
Here – 4 and + 4 cancelled to each other:
ð 5y < 11
Divide both sides by 5
ð y < 2.2
Now solve second inequality
y + 12 > 13
Now we subtract 12 from both sides:
y + 12 – 12 > 13 – 12
y > 1
In the next session we are going to discuss Inequalities and Read more maths topics of different grades such as Equations with no Solution in the upcoming sessions here.
We can define Compound Inequalities as the combination of two or more inequalities bound with the ‘and’ or ‘or’ symbol.
Let’s show you the example of inequalities:
Suppose two inequalities are given:
(a) 5y – 4 < 7
(b) y + 12 > 13
Then both the above inequalities can be represented as Compound Inequalities as:
5y – 4 < 7 and y + 12 > 13
The above representations of inequalities are known as compound inequalities or generally known as conjunction of inequalities.(want to Learn more about Inequalities, click here),
Example2: (a) 5y > 65
(b) m + 7 < 3
The above inequalities can be represented in below given format:
5y > 65 or m + 7 < 3
The above representations of inequalities are known as disjunction of inequalities. Now we show you how to solve the compound inequalities:
Example: Solve the given compound inequalities 5y – 4 < 7 and y + 12 > 13 ?
Solution: Here we solve the inequalities in different way:
=> 5y – 4 < 7
Now we add 4 in both sides
ð 5y – 4 + 4 < 7 + 4
Here – 4 and + 4 cancelled to each other:
ð 5y < 11
Divide both sides by 5
ð y < 2.2
Now solve second inequality
y + 12 > 13
Now we subtract 12 from both sides:
y + 12 – 12 > 13 – 12
y > 1
In the next session we are going to discuss Inequalities and Read more maths topics of different grades such as Equations with no Solution in the upcoming sessions here.
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