Identity vs Equation Math Example 1

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

Example 1

easy
Is 2(x+3)=2x+62(x + 3) = 2x + 6 an identity or an equation with specific solutions?

Solution

  1. 1
    Expand the left side: 2x+62x + 6.
  2. 2
    Compare: 2x+6=2x+62x + 6 = 2x + 6 is always true, regardless of xx.
  3. 3
    This is an identity—it holds for all values of xx.

Answer

Identity (true for all xx).
An identity is true for every value of the variable. An equation with specific solutions is true only for certain values. If simplifying both sides gives the same expression, it is an identity.

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 →

More Identity vs Equation Examples

Example 2 medium

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

Example 3 easy

Is [formula] an identity or an equation?

Example 4 medium

Is [formula] an identity?

← All Identity vs Equation Examples Identity vs Equation Concept