# What is linear equation | linear equation definition

In that article what is linear equation give the linear equation examples also linear equation definition and linear function examples also solving linear equations examples.

what is linear equation:

### Important things to remember :

1. Real numbers a and b (where a is not equal to zero) and x is a variable, So the equation ax + b = 0 is called one variable linear equation.
2. The left hand side of the equation ax + b = 0 is a linear polynomial and there is only one variable in that polynomial.
3. If a given equation converts to an equation of the form ax + b = 0, then it is said to be a linear equation in one variable.
4. The exponent of the x variable in the equation is one. These equations are like the general form of the linear equation ax + b = 0. So they are linear equations.

### Some Linear equation example :

1) 5x – 12 = 0
2) 7x + 6 = 9x – 4
3) x + 9 = 4x.

#### To Solve the equation :

1. The number by which both sides of the equation are equal in value. That number is said to satisfy the equation.
2. The number that satisfies the equation is called the solution of the equation.
3. The set of solutions of an equation is the set of solutions of that equation.

Ex 1) 2x = 18 then x =?
Ans. :
2x = 18
x = 18 / 2
therefore, x = 9.

Ex 2) 3x + 7 = 22 then x = ?
Ans. :
3x + 7 = 22
3x = 22 – 7
3x = 15
x = 15 / 3
therefore, x = 5.

Ex 3) x + 9 = 4x
Ans. :
x + 9 = 4x
9 = 4x – x
9 = 3x
x = 9 / 3
therefore , x = 3.

Ex 4) y – 4 = 3y – 10
Ans. :
10 – 4 = 3y – y
6 = 2y
y = 6 / 2
y = 3
therefore, y = 3.

Ex 5) ( 5x / 2 ) + 3 = 21 / 2
Ans. :
( 5x / 2 ) + 3 = 21 / 2
both sides multiples by 2, we get
5x + 6 = 21
5x = 21 – 6
5x = 15
x = 15 / 5
x = 3
therefore, x = 3.

Ex 6) ( y – 1 ) / 5 = y / 3
Ans. :
( y – 1 ) / 5 = y / 3
3 ( y – 1 ) = 5y
3y – 3 = 5y
3y – 5y = 3
– 2y  = 3
y = -3 / 2
therefore, y = – 3 / 2.