Inequalities

• What Are the Least and Greatest Values of x?
  For real x, y, and z, the possible values of x range from -1 to 13/3; both endpoints are attained when y equals z.
• Is This Inequality Always True for Positive x, y, z?
  The inequality is false for arbitrary positive x, y, z. See counterexamples and a simple proof under the sufficient condition x ≥ yz, y ≥ zx, and z ≥ xy.