Which of the following correctly explains why $x + 5 = 12$ is NOT an algebraic identity?

Class 8Algebraic Expressions and IdentitiesAlgebra

Step-by-Step Solution

No. It is true only when

x = 7

, not for ALL values of

x

. An identity must hold for every value of the variable.

Answer: A) It is true only when

x = 7

, not for all values of

x

Identities save time and reveal structure. Examples of clever uses:

- Compute

10 2^{2}

mentally:

(100 + 2)^{2} = 10 0^{2} + 2 (100) (2) + 2^{2} = 10000 + 400 + 4 = 10404

.
- Compute

99 \times 101 : (100 - 1) (100 + 1) = 10 0^{2} - 1^{2} = 10000 - 1 = 9999

.
- Compute

4 7^{2} - 4 3^{2} : (47 - 43) (47 + 43) = 4 \times 90 = 360

.

Look at any number-pair calculation; if you can rewrite it as one of the three identity forms, the answer falls out.

Don't just memorise the answer — build a daily practice habit.