\(\dfrac{11}{4}+\left|\dfrac{2}{7}-x\right|-\dfrac{5}{2}=\dfrac{4}{3}\)
\(\dfrac{11}{4}+\left|\dfrac{2}{7}-x\right|=\dfrac{4}{3}+\dfrac{5}{2}\)
\(\dfrac{11}{4}+\left|\dfrac{7}{2}-x\right|=\dfrac{23}{6}\)
\(\left|\dfrac{7}{2}-x\right|=\dfrac{23}{6}-\dfrac{11}{4}\)
\(\left|\dfrac{7}{2}-x\right|=\dfrac{13}{12}\)
Suy ra
\(\left\{{}\begin{matrix}\dfrac{7}{2}-x=\dfrac{13}{12}\Rightarrow x=\dfrac{7}{2}-\dfrac{13}{12}=\dfrac{29}{12}\\\dfrac{7}{2}-x=\dfrac{-13}{12}\Rightarrow x=\dfrac{7}{2}-\dfrac{-13}{12}=\dfrac{55}{12}\end{matrix}\right.\)
Vậy x \(\in\left\{\dfrac{29}{12};\dfrac{55}{12}\right\}\)
\(\dfrac{11}{4}+\left|\dfrac{2}{7}-x\right|-\dfrac{5}{2}=\dfrac{4}{3}\)
\(\left(\dfrac{11}{4}-\dfrac{5}{2}\right)+\left|\dfrac{2}{7}-x\right|=\dfrac{4}{3}\)
\(\left(\dfrac{11}{4}-\dfrac{10}{4}\right)+\left|\dfrac{2}{7}-x\right|=\dfrac{4}{3}\)
\(\dfrac{1}{4}+\left|\dfrac{2}{7}-x\right|=\dfrac{4}{3}\)
\(\left|\dfrac{2}{7}-x\right|=\dfrac{4}{3}-\dfrac{1}{4}\)
\(\left|\dfrac{2}{7}-x\right|=\dfrac{16}{12}-\dfrac{3}{12}\)
\(\left|\dfrac{2}{7}-x\right|=\dfrac{13}{12}\)
\(\dfrac{2}{7}-x=\pm\dfrac{13}{12}\)
\(TH1:\dfrac{2}{7}-x=\dfrac{13}{12}\)
\(x=\dfrac{2}{7}-\dfrac{13}{12}\)
\(x=\dfrac{24}{84}-\dfrac{91}{84}\)
\(x=-\dfrac{67}{84}\)
\(TH2:\dfrac{2}{7}-x=-\dfrac{13}{12}\)
\(x=\dfrac{2}{7}-\left(-\dfrac{13}{12}\right)\)
\(x=\dfrac{2}{7}+\dfrac{13}{12}\)
\(x=\dfrac{24}{84}+\dfrac{91}{84}\)
\(x=\dfrac{115}{84}\)
Vậy \(x=-\dfrac{67}{84},x=\dfrac{115}{84}\)
