Identity vs Equation Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Is 5x=205x = 20 an identity or an equation?

Solution

  1. 1
    Try x=4x = 4: 5(4)=205(4) = 20 โœ“. Try x=3x = 3: 5(3)=15โ‰ 205(3) = 15 \neq 20 โœ—.
  2. 2
    It is only true for x=4x = 4, so it is an equation (not an identity).

Answer

Equation (true only for x=4x = 4).
If a statement fails for even one value of the variable, it cannot be an identity. It is an equation with specific solutions.

About Identity vs Equation

An identity is an equation that holds true for all possible values of the variable, such as (a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2. A conditional equation is true only for specific values, like x+3=7x + 3 = 7 (true only when x=4x = 4).

Learn more about Identity vs Equation โ†’

More Identity vs Equation Examples

Example 1 easy

Is [formula] an identity or an equation with specific solutions?

Example 2 medium

Classify: (a) [formula] and (b) [formula].

Example 4 medium

Is [formula] an identity?

โ† All Identity vs Equation Examples Identity vs Equation Concept