Sunday, 12 February 2012

Solving Inequalities with Rational Numbers

Previously we have discussed about how to solve inequalities with fractions and Today I am going to discuss about solving inequalities by rational numbers which comes under cbse syllabus 12th. Before I start telling you the actual procedure to solve these inequalities by rational numbers, we should know about the inequalities and rational numbers. Inequality means unequal. If two quantities or parts or anything which are not equal then this leads to inequality. Inequality may arise if two quantities have a relation of greater than (>) or less than (<) or greater than equal to (>=) or less than equal to (<=).
Now we come to rational numbers. Rational numbers are basically the fraction of two numbers and have a form of a/b where a and b are two integers and b is not equal to 0.
Solving inequalities with rational numbers is a very interesting and easy task and can be practiced using Inequalities Worksheet. To solve this we must follow a simple procedure that is as follows:
1.      First of all to solve the equation we must get the variable alone on left side of the equation, so that we can find its value.
2.      Now to get the variable we must use an inverse operation. This inverse operation will undo whatever had been done to the variable.
3.      Here inverse operations are: addition and subtraction or multiplication and division.
4.      To maintain the equality we should do the same operation on both the sides.
Now to get this whole procedure let us take an example:
Here the question is to determine the value of y in the given equation:  3/2 y = 5/4
2/3 * (3/2) y = 2/3 * (5/4) [Multiply both the sides by 2/3]
y = 10/12
Now again solving this we will get y = 5/6.
So by using this procedure we can use rational numbers to solve inequalities. In the next session we will discuss Solving inequalities by addition and subtractions and Read more maths topics of different grades such as Multiplying Rational Expressions in the upcoming sessions here.   

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