How to determine whether an equation is always, sometimes , never, or true?

An equation is a proposition of two expressions that are equal.

First. An equation that is always true:

This is the case of an equation that the values on the left and right side of the equation are always the same. For instance:



That is:



This equation is always true because both expressions are equal to 8. The following equations are also always true, namely:



Second. An equation that is sometimes true.

This is the case of an equation that is true for some values of a variable (or variables). Then, our goal is to find these values. For instance:



Next, the value that guarantees the statement of truth is:



Finally, the value that makes the equation to be true is called the solution of the equation.

Third. An equation that is never true.

This is the case of an equation that is always false. For instance:



Therefore, the equation: