Question

What's the name of an inequality which is always true?

Answer 1

Answer:

An equation or an inequality that contains at least one variable is called an open sentence. When you substitute a number for the variable in an open sentence, the resulting statement is either true or false. If the statement is true, the number is a solution to the equation or inequality

Answer 2

Answer:

There is no name for such inequality.

For your information:

The examples of such inequality are AM-GM-HM, Cauchy-Schwarz inequality.

• $\frac{a+b}{2}\geq \sqrt{ab} \geq \frac{2ab}{a+b}$, for positive a, b
• $(a^2+b^2)(x^2+y^2)\geq (ax+by)^2$ for reals a, b, x, y