Tìm x biết: a) |x : (-5/6) - 3/4| = 2 b) |-2 : x + 5/6| = 3/4 c) |(-2/3).x

* Hướng dẫn giải

a) $\left|x:\left(-\frac{5}{6}\right)-\frac{3}{4}\right|=2\iff \left|-\frac{6}{5}x-\frac{3}{4}\right|=2$$\iff \left[\begin{array}{l}-\frac{6}{5}x-\frac{3}{4}=-2\\ -\frac{6}{5}x-\frac{3}{4}=2\end{array}\right.\iff \left[\begin{array}{l}x=\frac{25}{24}\\ x=-\frac{55}{24}\end{array}\right.$

b) Điều kiện $x\ne 0$

$\begin{array}{l}\left|-2:x+\frac{5}{6}\right|=\frac{3}{4}\iff \left[\begin{array}{l}-2:x+\frac{5}{6}=-\frac{3}{4}\\ -2:x+\frac{5}{6}=\frac{3}{4}\end{array}\right.\\ \iff \left[\begin{array}{l}\frac{-2}{x}=\frac{-19}{12}\\ \frac{-2}{x}=\frac{-1}{12}\end{array}\right.\iff \left[\begin{array}{l}x=\frac{24}{19}\\ x=24\end{array}\right.\end{array}$

c) $\left|\left(-\frac{2}{3}\right)x+\frac{3}{8}\right|.\left(-\frac{8}{5}\right)=-\frac{8}{15}\iff \left|-\frac{2}{3}x+\frac{3}{8}\right|=\frac{1}{3}$$\iff \left[\begin{array}{l}-\frac{2}{3}x+\frac{3}{8}=-\frac{1}{3}\\ -\frac{2}{3}x+\frac{3}{8}=\frac{1}{3}\end{array}\right.\iff \left[\begin{array}{l}x=\frac{17}{16}\\ x=\frac{1}{16}\end{array}\right.$

Vậy $x\in \left\{\frac{1}{16};\frac{17}{16}\right\}$