4. Tìm số hữu tỉ x, biết rằng:
a) $\left ( x-\frac{5}{3} \right ):-1\frac{3}{4}=0$
b) $\left ( x-\frac{1}{5} \right ).\left ( 1\frac{3}{5}+2x \right ) = 0$
c) $\left ( x-\frac{4}{7} \right ):\left ( x+\frac{1}{2} \right ) > 0$
d) $(2x-3):\left ( x+1\frac{3}{4} \right )<0$
5. Tìm số nguyên x, biết rằng:
$\left ( -1\frac{1}{2}:\frac{3}{-4} \right ).\left ( -4\frac{1}{2} \right )-\frac{1}{4} < \frac{x}{8} < \frac{-1}{2}.\frac{3}{4}:\frac{1}{8}+1$
Bài Làm:
4.
a) $\left ( x-\frac{5}{3} \right ):-1\frac{3}{4}=0$
$\Leftrightarrow x - \frac{5}{3}=0$
$\Leftrightarrow x=\frac{5}{3}$
b) $\left ( x-\frac{1}{5} \right ).\left ( 1\frac{3}{5}+2x \right ) = 0$
$\Leftrightarrow x-\frac{1}{5}=0$ hoặc $\frac{8}{5}+2x=0$
$\Leftrightarrow x=\frac{1}{5}$ hoặc $x=\frac{-4}{5}$
c) $\left ( x-\frac{4}{7} \right ):\left ( x+\frac{1}{2} \right ) > 0$
$\Leftrightarrow $ $\left\{\begin{matrix}x-\frac{4}{7}>0\\ x+\frac{1}{2}>0\end{matrix}\right.$ hoặc $\left\{\begin{matrix}x-\frac{4}{7}<0\\ x+\frac{1}{2}<0\end{matrix}\right.$
$\Leftrightarrow x>\frac{4}{7}$ hoặc $x<\frac{-1}{2}$
d) $(2x-3):\left ( x+1\frac{3}{4} \right )<0$
$\Leftrightarrow $ $\left\{\begin{matrix}2x-3>0\\ x+\frac{7}{4}<0\end{matrix}\right.$ hoặc $\left\{\begin{matrix}2x-3<0\\ x+\frac{7}{4}>0\end{matrix}\right.$
$\Leftrightarrow $ $\frac{-7}{4}<x<\frac{3}{2}$
5. $\left ( -1\frac{1}{2}:\frac{3}{-4} \right ).\left ( -4\frac{1}{2} \right )-\frac{1}{4} < \frac{x}{8} < \frac{-1}{2}.\frac{3}{4}:\frac{1}{8}+1$
Sau khi biến đổi ta được:
$-9\frac{1}{4}<\frac{x}{8}<-2$
$\Leftrightarrow -74 < x < -16$
Mà x nguyên nên ta có x $\in $ {-73; -72; -71; ...; 13; 14; 15}