Wednesday, 15 February 2012

Solving inequalities by addition and subtractions

Previously we have discussed about first order differential equation and In this session we are going to study about the inequalities and how to solve them that comes under cbse 12th syllabus. Let us define an equation. An equation is an expression that contains combination of numbers and variables and shows relationship between them. After that these expressions are written in both sides of equality sign. In grade VI we study about the Algebraic Equations and solve the problem of inequalities.
Inequalities in algebra means two variables are not equal that is x≠y. There are various types of symbol to show the inequalities between the two variables like >(greater than),<(less than),>=(greater than or equal to),<=(less than or equal to) etc. Here, we will be solving inequalities by addition and subtractions. We will add and subtract the numbers into the expression.(Know more about inequalities in broad manner, here,)
Example of equation is: 4y + 5 = 9
Let us see some examples of solving inequalities:
Solving inequalities by addition:
Example1: Solve x-7 >=15
Solution: Now we solve this by adding digit 7 to both sides of inequality
                  x-7 +7  >=15+7
                  We know that -7 +7 = 0 and 15 + 7 =22
                  Thus x >=22
Example2: Solve a – 13 >= 28
Solution: We solve this by adding digit 13 to both sides of inequality
                     a – 13 >= 28
                     a – 13 +13 >= 28+13
                      a >=41
 Solving inequalities by subtractions:
Example3: Solve inequality by suitable method for:
                      X + 5 >=10
Solution: We subtract 5 from both sides of inequality
                     X + 5 – 5 >= 10 - 5
                            X > = 5
Example 4: Remove the inequality by adding or subtracting the numbers for given equation
                         a + 1 >=7
Solution: Here we solve the equation by subtracting 1 from both sides of inequality
                        a + 1-1 >= 7 - 1
                         a >= 6

In the next topic we are going to discuss Solving Multi Step Inequalities and if anyone want to know about Simplifying Rational Expressions then they can refer to Internet and text books for understanding it more precisely.

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