Notes On Introduction to Simple Equations - CBSE Class 7 Maths

Variable
A variable is something that varies. A variable can take different numerical values; its value is not fixed. Variables are usually denoted by letters of the alphabet, such as x, y, z, l, m, n, p, q etc. Expressions are formed using variables.

Expression
Expressions are formed by performing the operations like addition, subtraction, multiplication and division on the variables.Value of an expression depends on the value of the variable using which the expression is formed.

Equation
An equation is a condition of equality between two mathematical expressions. It is a condition on a variable.
e.g. 2x - 3 = 5, 3x + 9 = 11, 4y + 2 = 12
Two expressions on both sides of the equation should have equal value and atleast one of the expressions must have a variable. An equation remains the same if the LHS and the RHS of the equation are interchanged.

The equality sign in an equation shows that the value of the expression to the left hand side is equal to the value of the expression to the right hand side. If there is some other sign other than the equality sign between the LHS and the RHS, it is not an equation.
e.g. 3x + 5 > 6 is not an equation.

Solution of an equation
The value of the variable for which the left hand side of an equation is equal to its right hand side is called the solution of that equation.
e.g. For the equation, 5x + 5 = 15, x = 2 is a solution.

When the same number is added to or subtracted from both the sides of a balanced equation, the value of the left hand side remains equal to its value on the right hand side. If the same mathematical operation is not done on both sides of a balanced equation, the balance is disturbed.


e.g. (1) 5x + 3 = 13
On adding 2 to both sides of the equation, we get
5x + 3 + 2 = 13 + 2
5x + 5 = 15

(2) On subtracting 2 from both sides of the equation, we get
5x + 3 - 2 = 13 - 2
5x + 1 = 11

When an equation is divided or multiplied on both the sides by a non-zero number, the value of the left hand side remains equal to its value on the right hand side.
e.g. (1) 5x + 3 = 13
On dividing both sides of the equation by 4, we get
(5x + 3) ÷ 4 = 13 ÷ 4

2) 5x + 1 = 13
On multiplying both sides of the equation by 4, we get
4(5x + 1) = 4(13)
20x + 4 = 52

Summary

Variable
A variable is something that varies. A variable can take different numerical values; its value is not fixed. Variables are usually denoted by letters of the alphabet, such as x, y, z, l, m, n, p, q etc. Expressions are formed using variables.

Expression
Expressions are formed by performing the operations like addition, subtraction, multiplication and division on the variables.Value of an expression depends on the value of the variable using which the expression is formed.

Equation
An equation is a condition of equality between two mathematical expressions. It is a condition on a variable.
e.g. 2x - 3 = 5, 3x + 9 = 11, 4y + 2 = 12
Two expressions on both sides of the equation should have equal value and atleast one of the expressions must have a variable. An equation remains the same if the LHS and the RHS of the equation are interchanged.

The equality sign in an equation shows that the value of the expression to the left hand side is equal to the value of the expression to the right hand side. If there is some other sign other than the equality sign between the LHS and the RHS, it is not an equation.
e.g. 3x + 5 > 6 is not an equation.

Solution of an equation
The value of the variable for which the left hand side of an equation is equal to its right hand side is called the solution of that equation.
e.g. For the equation, 5x + 5 = 15, x = 2 is a solution.

When the same number is added to or subtracted from both the sides of a balanced equation, the value of the left hand side remains equal to its value on the right hand side. If the same mathematical operation is not done on both sides of a balanced equation, the balance is disturbed.


e.g. (1) 5x + 3 = 13
On adding 2 to both sides of the equation, we get
5x + 3 + 2 = 13 + 2
5x + 5 = 15

(2) On subtracting 2 from both sides of the equation, we get
5x + 3 - 2 = 13 - 2
5x + 1 = 11

When an equation is divided or multiplied on both the sides by a non-zero number, the value of the left hand side remains equal to its value on the right hand side.
e.g. (1) 5x + 3 = 13
On dividing both sides of the equation by 4, we get
(5x + 3) ÷ 4 = 13 ÷ 4

2) 5x + 1 = 13
On multiplying both sides of the equation by 4, we get
4(5x + 1) = 4(13)
20x + 4 = 52

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