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

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:

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

**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:

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

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.

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