Equations and Inequalities in Grade III

Hello friends, Previously we have discussed about is 2 a rational number and in today's article we are going to discuss about the problems in equations and inequalities for grade III of CBSE math Syllabus. Here, I am going to tell you the best way of understanding the equations and inequalities problems. Start with the definition of equation, when two expressions are joined with the help of equal symbol then, it is called as equation. For example: x + 5=2, x + 4=1. Let me clear one thing that when we add, subtract, multiply, or divide the same number on both the side of the equation, the equal sign of an equation does not change. On other hand two algebraic expressions or two real numbers related by the symbol ‘<’, ‘>’, ‘<=’ or ‘>=’ form an inequality. For example: x-3>5. In inequalities perform addition or subtraction by the same number on both sides. Multiply or divide by the same number on both sides but if we divide or multiply by a negative number, we must reverse the inequality sign.
Now I would like to tell you that how would you solve the equations and inequalities problems. Firstly we are going for Problems in equations.
Example: Solve the equation for the variable y: y - 20 = 40
          Solution: y - 20 = 40
         Firstly we add 20 on both sides of the equation
          y – 20 + 20 = 40 + 20
         y = 60
        So, the answer is y = 60.
Example: Solve the equation for the variable: (y/3) + 50 = 40
            Solution :(y / 3) + 50 = 40
           Subtract 50 on both sides of the equation
          (y / 3) + 50 - 50 = 40 - 50
         (y / 3) = -10
        Multiply 3 on both sides of the equation
        (y / 3) * 3 = -10 * 3
        y = -30 so, the answer is 30

Now I am discussing about how to solve inequalities problems. Some examples are given below.(want to Learn more about Inequalities ,click here),
Example: Solve the inequality: 8x + 4 < 6x +7.
Solution: We have, 8x + 4 < 6x +7
Subtract 6x on both sides of the equation
8x – 6x + 4 < 6x + 7 – 6x
2x + 4 < 7
Subtract 4 on both sides of the equation
2x + 4 – 4 < 7 – 4
2x < 3
Divide by 2 on both sides of the equation
x < 3/2
So from the above all the real numbers are greater than 1. Hence, the solution set is (-infinity, 3/2).
Example: Solve the inequality: -2x – 7 < 7
Solution: -2x-7<7
Add 7 on both sides of the equation
-2x - 7 + 7 <7 + 7
-2x < 14
Divide by-2 on both sides of the equation and you will see the inequality sign is to be reversed.
x > -7
So from the above all real numbers are greater than -7 and hence, the solution set is (-7, infinity).

So this is all about equations and inequalities and if anyone want to know about

Time in terms of unit fractions then they can refer to Internet and text books for understanding it more precisely. You can also refer 4th Grade blog to study about Multiplication and division situations.

How to deal with Expressions in grade III

Hello friends, today we are going to discuss a very interesting topic, expressions, equations, and inequalities which are included in grade III of maharashtra state board of secondary and higher secondary education. Friends, as we all know study of mathematics is almost impossible without equations, expressions and inequalities, let’s start with expressions. An expression shows a math relationship between variables and constants, one interesting thing about expression is that it does not have a solution or answer if it is represented alone. It can only be evaluated by substituting the value of variable, we can solve an expression only if it is related by a equation or an inequality, for example: 5x +6 is an expression in one variable it can be evaluated by substituting different values of x, lets put x=5 then we obtain the value of expression = 31, this is called the evaluation of the expression.
Equation is nothing but a statement that shows two expressions are equal and expressions can be algebraic expression or any other, an equation consists of a number of variable and non variable, variables are the quantities which can have many possible values such as length, time, height etc. Non variables are those quantities whose value remain constant with time such as numerical digits whereas unknown are those quantities whose value is to be determine from the equation. Solution of an equation refers to find the value of unknown present in the equation. Friends, here we have an example of equation X+Y = 7, is an  linear equation having two variable whose sum is equal to 7, an equation can have a number of solutions, for example the solution for above equation can be found out by putting  x=2 and y=5,  other solutions to this equations are  (0,7) (-2,9)  and there can be a number of other solutions.

Now let’s know about inequalities, two expressions or real numbers separated by ‘<’, or ‘>’ , ‘<=’ or ‘>=’ sign form an inequality. Below are some steps on how to solve inequalities:

1. First we add or subtract the same number on both sides to reduce the size of the inequality
2. Then we separate the variables and constant of inequality
3. Then we multiply or divide by same number on both sides to get the solution of the inequality.

Now we consider few examples which will surely help you to understand the topic and for more information about this topic refer this:
Ex. Solve the inequality 8x+5 < 6x+7.
Subtracting 6x from both sides of the inequality, we obtain
8x-6x+5 < 6x-6x+7 or
2x+5 < 7 or
2x< 7-5 or 2x<2or
X<1 this is our answer.

Here we take another example:
Solve the inequality 4x +2 < -2x+ 14,
First of all we subtract 2 from both sides 4x+2-2 < -2x+14-2 or
4x < -2x +12 now we add 2x t both sides and we obtain

4x+2x < -2x +2x +12 or

6x < 12 now we divide both sides of the inequality by 6 and we obtain

x < 2 this is our answer.

Friends that is all for today and if you want to get information about Numbers and Operations and another topic from grade III that is  Fractions and decimals you all are advised to refer the internet.