Identities

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 2 + 20 = 10 + 20 =30 Thus the values of the two sides of the equality are equal when x = 2.

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 10 + 20 = 50 + 20 =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.

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 5 - 10 = 40 - 10 = 30 RHS = 4x + 10 = 4 x 5 + 10 = 20 + 10 = 30 Thus the values of the two sides of the equality are equal when x = 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 10 - 10 = 80 - 10 = 70 RHS = 4x + 10 = 4 x 10 + 10 = 40 + 10 = 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.

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