Inequalities

Previously we have discussed about variables and expressions worksheets and In today's session we are going to discuss about Inequalities which is a part of ap state intermediate board, In this part we Simplify expressions and statements. Some of them are equal to each other and some of them are not equal to each other. Inequalities contain those expressions and statements that are not equal to each other, they can be strictly greater than and only greater than, strictly less than and only less than and not equal too, but they cannot be equal. Some notations that are used in inequalities are:-
-The sign x < y denotes that x is less than y.
-The sign x > y denotes that x is greater than y.
-The sign x != y denotes that x is not equal to y. But in this notation we cannot say that which is greater than or less than to each other.
In all the above mentioned statements x is not equal to y, it means that they are strict inequalities. Let’s see more inequality statements that are not strict.
-The x ≤ y statement means that x is less than or equal to y.
-The x ≥ y statement means that x is less than or equal to y
We can use more inequalities statements that are much strict, they are:-
- The x << y means x is much less than y.
-The x >> y means x is much greater than y.
Now the question arises how to solve inequalities, to solve this we have to follow some procedure that is:-
-First of all same number should be add and subtract from both sides.
-Secondly shifting the sides and changing the adjustment of inequality sign.
-The same positive number should be multiply/divide from both the ends.
-The same negative number should be multiply/divide from both the ends and changing the adjustment of inequality sign.(Know more about Inequalities in broad manner, here,)
Remembering above rules helps to solve inequalities in an easy manner.
In the next session we are going to discuss Compound Inequalities
and if anyone want to know about Equations with no Solution then they can refer to Internet and text books for understanding it more precisely.

Compound Inequalities

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.