Tìm \(x\) biết: \(\left| {2x - 7} \right| - \left| { - \frac{3}{2}} \right| = 7\) \(\frac{3}{4} + \frac{1}{4}:x = - 3\)

* Hướng dẫn giải

\(\left| {2x - 7} \right| - \left| { - \frac{3}{2}} \right| = 7\)

\(\begin{array}{l}\left| {2x - 7} \right| - \left| { - \frac{3}{2}} \right| = 7\\\left| {2x - 7} \right| - \frac{3}{2} = 7\\\left| {2x - 7} \right| = 7 + \frac{3}{2}\\\left| {2x - 7} \right| = \frac{{17}}{2}\end{array}\)

Trường hợp 1:

\(\begin{array}{l}2x - 7 = \frac{{17}}{2}\\2x = \frac{{17}}{2} + 7\\2x = \frac{{31}}{2}\\x = \frac{{31}}{4}\end{array}\)

Trường hợp 2:

\(\begin{array}{l}2x - 7 =  - \frac{{17}}{2}\\2x =  - \frac{{17}}{2} + 7\\2x =  - \frac{3}{2}\\x =  - \frac{3}{4}\end{array}\)

Vậy \(x \in \left\{ { - \frac{3}{4};\,\,\frac{{31}}{3}} \right\}\).