# Real Numbers And Their Chain Of Inequalities

Algebra Level 3

$(A){ \quad x\, \, { < }\, \, x }^{ 2 }\, \, { < }\, \, { x }^{ 3 }\\ { (B)\quad x\, \, { < }\, \, x }^{ 3 }\, \, { < }\, \, { x }^{ 2 }\\ { (C)\quad x }^{ 2 }\, \, { < }\, \, x\, \, { < }\, \, { x }^{ 3 }\\ { (D)\quad x }^{ 2 }{ \, \, { < }\, \, x }^{ 3 }\, \, { < }\, \, x\\ (E)\quad { x }^{ 3 }\, \, { < }\, \, { x\, \, { < }\, \, x }^{ 2 }\\ (F){ \quad x }^{ 3 }{ \, \, { < }\, \, x }^{ 2 }\, \, { < }\, \, x$

If $x$ is a real number, how many of the above inequalities can be true?

×