Linear Equation in One Variable

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Linear equation in one variable is a statement of equality that involves only one variable
( unknown numbers).



Any value of the variable that satisfies the given equation is called a Solution or root of the equation.
Rules for solving equation in One Variable

1) Add the same number on both sides of the equation.
2) Subtract the same number from both sides of the equation.
3) Multiply both sides of the equation by the same non-zero number.
4) Divide both sides of the equation by the same non-zero number.
These rules are applied in such a way that on one side there should be only a variable.
The equality symbol (=) in the equation remains unchanged.

Note : In solving linear equations, we have to use a opposite operations.
x + 5 = 12
As there is + 5 so use opposite
operation and add -5 on both sides.
x + 5 = 12
- 5 = - 5
--------------------
x = 7

Check : For x = 7;
Left side = 7 + 5 = 12 = Right side

x - 5 = 12
As there is - 5 so use opposite
operation and add +5 on both sides.
x - 5 = 12
+ 5 = + 5
--------------------
x = 17

Check : For x = 17;
Left side = 17 - 5 = 12 = Right side

4m = 16
As there is 4 times m so divide both
side by 4.
4m 16
---- = -----
4 4
m = 4

Check : For m = 4 ;
Left side = 4 x 4 = 16 = Right side.
m
----- = 16
4
As there is m over 4 (division) So multiply both side by 4
m
4 x ------ = 16 x 4
4
m = 64

Check : For m = 64
Left side = 64 / 4 = 16 = Right side

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