Linear Equation

Look at these situations

Rajesh has 8 toffees

Guddu gave him some more toffees

Unknown number of toffees

We write

Similarly, there were 25 mangoes in a basket. Some mangoes were rotten which were removed. Now there are 18 mangoes.

25 mangoes

Some rotten mangoes

18 Good mangoes

Unknown number of mangoes

The mathematical statements 8 + x = 12 and 25 – x = 18 have the sign of equality (=) are called equations.

A statement of equality which contains literal numbers (variables) is called an equation.

Look at these equations

x +4 =20 2

x +9 x = 25 3

4x

+

5

Expression of Left Hand Side

LHS

=

13 Expression of Right Hand Side

RHS

Example I.

5 added to a number x is 17 We write

Example II. We write

5 + x = 17

2 times a number x is 16 2x = 16

Let us solve the equation

To find the value of x, we have to eliminate 9 from L.H.S.

So we have to eliminate an equal number from the R.H.S.

Given:

x + 9 =16 x + 9 – 9 = 16 – 9

∴

Adding -9(The additive inverse of 9) to both sides

Remember the following points while  Add the same number to both sides of the equation. solving an equation.  Subtract the same number from both sides of the equation.  

Multiply both sides of the equation by the same number (non zero). Divide both sides of the equation by the same number (non zero).

Query:6. Which of the following are equations? i. ax + b = 0 ii. 3x + 5 iii. 5x + 2b = 7a 8. Which of the following are linear equations? i. 3x2+2x+1=0 ii. 15x+7=0 iii. 3x+4=2x+5

iv. x3+x2+x+7=0

Presented by Guidence & Material provided by

Sh. Raj Kumar (Math Master) Implementation on Computer by Sandeep Singh Computer Faculty Govt. Saragarhi Memorial. Sec. School, Town Hall , Amritsar. This material is obtained from Subject book of Maths