Question

An equation that is satisfied for every value of the variable for which both sides are defined

Answer 1

An equation that is satisfied for every value of the variable for which both sides are defined is called an identity.

For example:
Given the equation
3x + 4 = x + 2(x + 2)

Notice that for any value of x you use, the equation is true.

Thus, this type of equation is called an identity.