Statement 1: If $2x \ge 3y$ and $3x = 4z$, then $9y > 8z$.

• Interpretation:

  1. $2x \ge 3y$
  2. $3x = 4z \Longrightarrow x = \frac{4z}{3}$

  Substituting $x = \frac{4z}{3}$ in $2x \ge 3y$:

  • $2(\frac{4z}{3}) \ge 3y$
  • $\frac{8z}{3} \ge 3y \Longrightarrow 8z \ge 9y$

  This implies $9y \le 8z$, which contradicts $9y > 8z$.

• Conclusion: Statement 1 is incorrect.

Statement 2: If $x < 2y$ and $y \le z$, then $x \le z$.

• Interpretation:

  1. $x < 2y$
  2. $y \le z$

  From the above, $x < 2y$ does not guarantee $x \le z$ because $z$ depends on $y$, and $x$ could still be greater than $z$.

• Conclusion: Statement 2 is incorrect.