a) \(2\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|-\dfrac{3}{2}=\dfrac{1}{5}\)
\(2\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|=\dfrac{1}{5}+\dfrac{3}{2}\)
\(2\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|=\dfrac{17}{10}\)
\(\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|=\dfrac{17}{10}:2\)
\(\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|=\dfrac{17}{20}\)
\(\circledast\)TH1: \(\dfrac{1}{2}x-\dfrac{1}{3}=\dfrac{17}{20}\)
\(\dfrac{1}{2}x=\dfrac{17}{20}+\dfrac{1}{3}\)
\(\dfrac{1}{2}x=\dfrac{71}{60}\)
\(x=\dfrac{71}{60}:\dfrac{1}{2}\)
\(x=\dfrac{71}{30}\)
\(\circledast\)TH2: \(\dfrac{1}{2}x-\dfrac{1}{3}=-\dfrac{17}{20}\)
\(\dfrac{1}{2}x=-\dfrac{17}{20}+\dfrac{1}{3}\)
\(\dfrac{1}{2}x=-\dfrac{31}{60}\)
\(x=-\dfrac{31}{60}:\dfrac{1}{2}\)
\(x=-\dfrac{31}{30}\)
Vậy \(x\in\left\{\dfrac{71}{30};-\dfrac{31}{30}\right\}\).
b) \(\dfrac{3}{4}-2\left|2x-\dfrac{2}{3}\right|=2\)
\(2\left|2x-\dfrac{2}{3}\right|=\dfrac{3}{4}-2\)
\(2\left|2x-\dfrac{2}{3}\right|=-\dfrac{5}{4}\)
\(\left|2x-\dfrac{2}{3}\right|=-\dfrac{5}{4}:2\)
\(\left|2x-\dfrac{2}{3}\right|=-\dfrac{5}{8}\) (vô lí)
Vậy \(x\in\varnothing \).
c) \(\left(3x-1\right)\left(-\dfrac{1}{2}x+5\right)=0\)
\(\circledast\)TH1: \(3x-1=0\)
\(3x=0+1\)
\(3x=1\)
\(x=\dfrac{1}{3}\)
\(\circledast\)TH2: \(-\dfrac{1}{2}x+5=0\)
\(-\dfrac{1}{2}x=0-5\)
\(-\dfrac{1}{2}x=-5\)
\(x=-5:\left(-\dfrac{1}{2}\right)\)
\(x=10\)
Vậy \(x\in\left\{\dfrac{1}{3};10\right\}\).
