$\text{Giải thích các bước giải:}$
$* \dfrac{-3}{6} = \dfrac{x}{-2} = \dfrac{-18}{y} = \dfrac{-z}{24}$
$⇒ \dfrac{-3}{6} = \dfrac{x}{-2} = \dfrac{-18}{y} = \dfrac{-z}{24}$
⇒ $\left[\begin{array}{ccc}\dfrac{-3}{6} = \dfrac{x}{-2}\\\dfrac{-3}{6} = \dfrac{-18}{y}\\\dfrac{-3}{6} = \dfrac{-z}{24}\end{array}\right]$
⇒ $\left[\begin{array}{ccc}\\6x = (-3) × (-2)\\-3y = (-18) × 6\\-6z = (-3) × 24\end{array}\right]$
⇒ $\left[\begin{array}{ccc}\\6x = 6\\-3y = -108\\-6z = -72\end{array}\right]$
⇒ $\left[\begin{array}{ccc}\\x = 1\\y = 36\\z = 12\end{array}\right]$
$* \dfrac{-8}{3} + \dfrac{-1}{4} < x < \dfrac{-2}{7} + \dfrac{-5}{7}$
$⇒ \dfrac{-32}{12} + \dfrac{-3}{12} < x < \dfrac{-2}{7} + \dfrac{-5}{7}$
$⇒ \dfrac{-35}{12} < x < -1$
$⇒ \dfrac{-35}{12} < x < \dfrac{-12}{12}$
$\text{Mà x ∈ Z}$
$⇒ x = -2$
$\text{Chúc bạn học tốt !}$
