Inequalities:
Introduction to inequalities:
In mathematics, an inequality is a statement about the relative size or order of two objects, or about whether they are the same or not.
* The notation a < b means that a is less than b.
* The notation a > b means that a is greater than b.
* The notation a ≠ b means that a is not equal to b, but does not say that one is greater than the other or even that they can be compared in size.
In each statement above, a is not equal to b. These relations are known as strict inequalities. The notation a < b may also be read as "a is strictly less than b".
In contrast to strict inequalities, there are two types of inequality statements that are not strict.
* The notation a ≤ b means that a is less than or equal to b (or, equivalently, not greater than b)
* The notation a ≥ b means that a is greater than or equal to b (or, equivalently, not less than b).
This was a very general view about the meaning of Inequalities,now let us understand the look at a more definite explanation,An inequalities is a statement, that relates the size or order of two objects or about whether they are the same or not.Solving linear inequalities is very much similar to solving linear equations, except for one small but important change: you flip the inequality sign whenever you multiply or divide the inequality by a negative number. In linear equation we don’t do that.
Procedure for Solving Inequalities:
As in the case of solving inequalities equations, there are certain rules for the inequality problems which do not change the solutions. Here is a list of "permissible'' manipulations:
Step1: Adding/subtracting the same number on both sides.
Step2: Switching sides and changing the orientation of the inequality sign.
Step3: Multiplying/dividing by the same positive number on both sides.
Step4: Multiplying/dividing by the same negative number on both sides and changing the orientation of the inequality sign.
* The notation a < b means a is less than b.
* The notation a > b means a is greater than b.
* The notation a ≠ b means a is not equal to b,
* The notation a ≤ b means a is less than or equal to b (or, equivalently, not greater than b)
* The notation a ≥ b means a is greater than or equal to b
Inequalities - Example Problems:
Solving inequalities for Addition and Subtraction:
1. 4x+2 < -2x+14
Solution:
4x+2-2 < -2x+14-2
4x < -2x+12
4x+2x < -2x+2x+12
6x < 12
6x /6< 12/6
x < 2
Hope you like the above example of Inequalities.Please leave your comments, if you have any doubts.
Introduction to inequalities:
In mathematics, an inequality is a statement about the relative size or order of two objects, or about whether they are the same or not.
* The notation a < b means that a is less than b.
* The notation a > b means that a is greater than b.
* The notation a ≠ b means that a is not equal to b, but does not say that one is greater than the other or even that they can be compared in size.
In each statement above, a is not equal to b. These relations are known as strict inequalities. The notation a < b may also be read as "a is strictly less than b".
In contrast to strict inequalities, there are two types of inequality statements that are not strict.
* The notation a ≤ b means that a is less than or equal to b (or, equivalently, not greater than b)
* The notation a ≥ b means that a is greater than or equal to b (or, equivalently, not less than b).
This was a very general view about the meaning of Inequalities,now let us understand the look at a more definite explanation,An inequalities is a statement, that relates the size or order of two objects or about whether they are the same or not.Solving linear inequalities is very much similar to solving linear equations, except for one small but important change: you flip the inequality sign whenever you multiply or divide the inequality by a negative number. In linear equation we don’t do that.
Procedure for Solving Inequalities:
As in the case of solving inequalities equations, there are certain rules for the inequality problems which do not change the solutions. Here is a list of "permissible'' manipulations:
Step1: Adding/subtracting the same number on both sides.
Step2: Switching sides and changing the orientation of the inequality sign.
Step3: Multiplying/dividing by the same positive number on both sides.
Step4: Multiplying/dividing by the same negative number on both sides and changing the orientation of the inequality sign.
* The notation a < b means a is less than b.
* The notation a > b means a is greater than b.
* The notation a ≠ b means a is not equal to b,
* The notation a ≤ b means a is less than or equal to b (or, equivalently, not greater than b)
* The notation a ≥ b means a is greater than or equal to b
Inequalities - Example Problems:
Solving inequalities for Addition and Subtraction:
1. 4x+2 < -2x+14
Solution:
4x+2-2 < -2x+14-2
4x < -2x+12
4x+2x < -2x+2x+12
6x < 12
6x /6< 12/6
x < 2
Hope you like the above example of Inequalities.Please leave your comments, if you have any doubts.
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