Tìm x biết |3x/5|=|-1/6|

a) \(|\dfrac{3}{5}x|=|-\dfrac{1}{6}|\)

\(\Rightarrow|\dfrac{3}{5}x|=\dfrac{1}{6}\)

\(\Rightarrow\dfrac{3}{5}x=\dfrac{1}{6}\) hoặc \(\dfrac{3}{5}x=-\dfrac{1}{6}\)

\(\Rightarrow x=\dfrac{1}{6}:\dfrac{3}{5}\) hoặc \(x=-\dfrac{1}{6}:\dfrac{3}{5}\)

\(\Rightarrow x=\dfrac{1}{6}.\dfrac{5}{3}\) hoặc \(x=-\dfrac{1}{6}.\dfrac{5}{3}\)

\(\Rightarrow x=\dfrac{5}{18}\) hoặc \(x=-\dfrac{5}{18}\)

b) \(|2x-3|+0,5=\dfrac{1}{3}:2\)

\(\Rightarrow|2x-3|+\dfrac{1}{2}=\dfrac{1}{3}.\dfrac{1}{2}\)

\(\Rightarrow|2x-3|+\dfrac{1}{2}=\dfrac{1}{6}\)

\(\Rightarrow|2x-3|=\dfrac{1}{6}-\dfrac{1}{2}=-\dfrac{1}{3}\)

Vì \(|2x-3|\ge0\forall x\)

=> Không tồn tại x thỏa mãn

c)\(|x-\dfrac{5}{6}|=2\left(x+\dfrac{1}{2}\right)\)

\(\Rightarrow|x-\dfrac{5}{6}|=2x+1\)

\(\Rightarrow x-\dfrac{5}{6}=2x+1\) hoặc \(x-\dfrac{5}{6}=-2x-1\)

\(\Rightarrow-\dfrac{5}{6}-1=2x-x\) hoặc \(-\dfrac{5}{6}+1=-2x-x\)

\(\Rightarrow-\dfrac{11}{6}=x\) hoặc \(\dfrac{1}{6}=-3x\)

\(\Rightarrow x=-\dfrac{11}{6}\) hoặc \(x=\dfrac{1}{6}:\left(-3\right)=\dfrac{1}{6}.\left(\dfrac{1}{-3}\right)=\dfrac{1}{-18}\)