1. Identities

2. An equation which is true for all possible values of the variable
is called an Identity.
Example1: Check if 5(x + 4) = 5x + 20 is an identity
Solution
We evaluate both the sides of this equality for some value of x, say x = 2.
For x = 2, LHS = 5(x + 4) = 5 x (2 + 4) =5 x 6=30
RHS= 5x + 20 = 5 x = =30
Thus the values of the two sides of the equality are equal when x = 2.

3. For x = 10, LHS = 5(x + 4) = 5 x (10 + 4) =5 x 14=70
Cont…
Let us now take, x =10.
For x = 10, LHS = 5(x + 4) = 5 x (10 + 4) =5 x 14=70
RHS= 5x + 20 = 5 x = =70
Thus the values of the two sides of the equality are equal when x = 10.
If LHS = RHS is true for every value of the variable in it,
then it is called as an Identity.
Thus, 5(x + 4) = 5x + 20 is an identity.

4. Example2: Check if 8x - 10 = 4x + 10 is an identity Solution
We evaluate both the sides of this equality for some value of x, say x = 5.
For x = 5, LHS = 8x - 10 = 8 x = = 30
RHS = 4x + 10 = 4 x = = 30
Thus the values of the two sides of the equality are equal when x = 5.

5. If LHS = RHS is not true for every value of the variable in it,
Cont…
Let us now take, x =10.
For x = 10, LHS = 8x - 10 = 8 x = = 70
RHS = 4x + 10 = 4 x = = 50
Thus the values of the two sides of the equality are not equal when x = 5.
If LHS = RHS is not true for every value of the variable in it,
then it is not an identity.
Thus, 8x - 10 = 4x + 10 is not an identity.

6. Try these
Check if the following are identities
4n-5 = 3n-1
(5 + x) ( 5 - x) = 25 - x2