Tìm x , biết: a) trị tuyệt đối của ( 2 x − 1 /3 ) + 3 /2 = 2 ;
Giải thích
a) \[\left| {2x - \frac{1}{3}} \right| + \frac{3}{2} = 2\]
\[\left| {2x - \frac{1}{3}} \right| = 2 - \frac{3}{2}\]
\[\left| {2x - \frac{1}{3}} \right| = \frac{1}{2}\]
TH 1: \[2x - \frac{1}{3} = \frac{1}{2}\]
\[2x = \frac{1}{2} + \frac{1}{3}\]
\[2x = \frac{3}{6} + \frac{2}{6}\]
\[2x = \frac{5}{6}\]
\[x = \frac{5}{{12}}\]
TH 2: \[2x - \frac{1}{3} = - \frac{1}{2}\]
\[2x = - \frac{1}{2} + \frac{1}{3}\]
\[2x = - \frac{3}{6} + \frac{2}{6}\]
\[2x = - \frac{1}{6}\]
\[x = \frac{{ - 1}}{{12}}\]
Vậy \[x \in \left\{ {\frac{5}{{12}};\frac{{ - 1}}{{12}}} \right\}\].