lean_workbook_plus_40697

Given three real positive numbers $x,y,z$ that satisfy the following set of inequalities: \n(1) $\frac{11}{6}z < x + y < 2z$ , \n(2) $\frac{3}{2}x < y + z < \frac{5}{3}x$ , \n(3) $\frac{5}{2}y < x + z < \frac{11}{4}y$. Prove that $y < x < z$.