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.

Math Blog on Solving inequalities by addition and subtraction

In the mathematical aspect solving inequalities by addition and multiplication is a simpler task, when you are little bit aware of equations and their functionality. Equations are nothing but an expression in both sides of equal sign, which are written in math format and check the equality & inequality from the expression. Now focusing on solving inequalities by addition and subtractions is just placing the values in both sides of equal sign.  (To get help on central board of secondary education click here)

                      Example: A + 5 = 14
This is the example of equation which shows the mathematical expressions in the both sides of equal sign. Here we have to calculate the value of A by adding or subtracting the numbers in both sides of equal sign. Now we are focusing on solving the inequalities of equation by addition and subtraction. Solving inequalities by addition and subtraction some examples are given below:
 Example:  a – 6 = 18            
                Now if we follow the addition rule (according to addition rule if x=y then x+a = x+y) i.e. add some number in both sides of equal sign to remove the inequality from the equation. Then in next step equation will be
                a – 6 + 6 = 18 + 6
                    a = 24
Now if we want to find out that obtained solution is correct or not then we can do that by putting the obtained answer into the initial equation. It means put a = 24 in the initial equation.
                Initial equation is   a – 6 = 18
                                              24 – 6 = 18
                                                  18 = 18
We can see that both sides of equation have same value then we can say that our obtained result is correct. The above example shows the way of solving inequality by addition. Now we see solving inequalities by subtractions.
Example 2:      solve z + 10 = 17
                  Now we solve this inequality by subtracting the values from both sides of equal sign.
Then equation will be         z + 10 – 10 = 17 – 10
                                                        z = 7
  In the next topic we are going to discuss Solving Inequalities by Multiplying and Dividing and In the next session we will discuss about Math Blogs on Solving two step linear equations.