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.

Graphing Linear Inequality

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Today we all are going to learn about the basic concept behind Inequality. An inequality tells that two values are not equal. For example a ≠ b shows that a is not equal to b. A linear inequality describes an area of the coordinate plane that has a boundary line. In simple way in linear inequality graphs everything is on one side of a line on a graph.

In mathematics a linear inequality is an inequality which involves a linear function. To solve Inequalities we must remember the symbols showing inequalities like the symbol < means less than and the symbol > means greater than and the symbol ≦ or ≤ less than or equal to etc.

Slope formula plays an important role in graphing linear inequalities. So we need to know what slope formula means. Slope of a line describes the steepness, incline or grade of the straight line. Let's take an example to understand the linear inequalities:

Example: -8 < 2x - 4 < 16

add 4 to all 3 parts

-4 < 2x < 20

divide 2 from all 3 parts

-2 < x < 10

To graph the following equation, you put an open circle or we can say mark it by a dot on the point

(-2,0) and then you put an open circle on the point (10,0).Then draw a line between the two.