Tìm x biết: \(\left| {2x - 1} \right| - \dfrac{1}{2} = \dfrac{1}{3}\)

* Hướng dẫn giải

Ta có:

\(\left| {2x - 1} \right| - \dfrac{1}{2} = \dfrac{1}{3}\)

\(\begin{array}{l}\left| {2x - 1} \right| = \dfrac{1}{3} + \dfrac{1}{2}\\\left| {2x - 1} \right| = \dfrac{5}{6}\end{array}\)

+) TH1: \(2x - 1 = \dfrac{5}{6}\)

\(\begin{array}{l}2x = \dfrac{5}{6} + 1\\2x = \dfrac{{11}}{6}\\x = \dfrac{{11}}{6}:2\\x = \dfrac{{11}}{{12}}\end{array}\)

+) TH2: \(2x - 1 = - \dfrac{5}{6}\)

\(\begin{array}{l}2x = - \dfrac{5}{6} + 1\\2x = \dfrac{1}{6}\\x = \dfrac{1}{6}:2\\x = \dfrac{1}{{12}}\end{array}\)

Vậy \(x = \dfrac{{11}}{{12}} \,\, hoặc \,\, x = \dfrac{1}{{12}}\)