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.

Equations and Inequalities

Previously we have discussed about rational expression calculator and In today's session we are going to discuss about Equations and Inequalities which comes under cbse books for class 11,  Equations are defined as the combination of number and variables that have an equal sign and both sides of an equation must be equal to each other .To solve the equation or for finding the values of variable of a equation are same in meaning .It means that when find the values in form of real number and when it is substituted then it will provide the identity as an example a given equation
3 ( a + 4 ) = -4 ( 2 – 2 a )
By simplify it we get
3 a + 12 = - 8 - 8 a
- 5 a = - 20
a = 4 ( dividing the both side of equation by – 5 ) .
But when we talk about the inequalities, all the rules of equations will be applied except some of the rules of division or multiplication by a negative number .inequalities can be understood by an example :
3 < 4 is multiplied by - 5 then it gives
3 * - 5 > 4 * - 5
- 15 > - 20 means in solving the inequality or finding the values of the variable the solution belongs to an interval of real numbers . (Know more about  Inequalities in broad manner, here,)
Some example of inequalities that describe the rules are as follows :
example : An inequality - ( 3 + a ) < 2 ( 3 a + 2 )
By simplifying it we get
-3 – a < 6 a + 4
-a – 6 a < 4 + 3
- 7 a < 7
By dividing the ( - 7 ) , we get a > -1 . In form of interval notation it is written as ( - 1 , infinity ).
In the next session we are going to discuss Compound Inequalities and Read more maths topics of different grades such as Rationalizing the Denominator in the upcoming sessions here.

Solving Multi Step Inequalities

Previously we have discussed about statistics worksheets and In today's session we are going to discuss about Solving Multi step inequalities which is a part of cbse 11th syllabus and is same like Solving Multistep Equations, It includes one or more operations that can be solved by avoiding the operations in reverse order. It is just like solving the equations with one or more than one operations. An inequality or an equation with one or more operations has two steps to solve it that are as follows:
( a ) By taking the inverse of addition or subtraction .
( b ) By using the inverse of division or multiplication for simplifying it.
It should be remembered at the time of solving the inequalities that while multiplying or dividing with the negative numbers the symbol of inequalities is reversed.
We can take an example for describe the process of solving the inequalities:
Here we take an equation with two step inequalities that means it has two operations and has two step solutions : 3 p – 10 >= 14
Here in two step solutions, we start with the variable p and understand it step by step .(want to Learn more about Inequalities, click here),
In the above equation variable p is multiplied with number 3 as ' 3*p ' and then number 10 is subtracted from the term 3p as 3 p - 10 . After it getting the answer 14 that is written as
3 p -10 > 14 .So there are steps that follow is start with the variable p then multiply by 3 then subtract 10 and at last equal to 14 .
So , for solving an inequality goes from the backward side and using the reverse operations. Start with the last step that is result 14 .
Now , by follow the reverse process, 10 is added to the 14 means 14 + 10 that is the reverse process of the subtracting 10 .
Next , the inverse of multiplying by 3 is divide by the 3 that is p > = ( 14 + 10 ) / 3
p > = 24 / 3
p > = 8 .
At last 8 is the answer of given inequality that is greater than equal to 8 .
In the next session we are going to discuss Equations and Inequalities and if anyone want to know about Math Blog on Subtracting Rational Expressions then they can refer to Internet and text books for understanding it more precisely.