Question

\(\left|\dfrac{1}{2}-x\right|-1\dfrac{2}{3}=0.5\)

Answer 1

\(\left|\dfrac{1}{2}-x\right|-1\dfrac{2}{3}=0,5\)

\(\Leftrightarrow\left|\dfrac{1}{2}-x\right|=0,5+1\dfrac{2}{3}\)

\(\Leftrightarrow\left|\dfrac{1}{2}-x\right|=\dfrac{1}{2}+\dfrac{5}{3}\)

\(\Leftrightarrow\left|\dfrac{1}{2}-x\right|=\dfrac{3}{6}+\dfrac{10}{6}\)

\(\Leftrightarrow\left|\dfrac{1}{2}-x\right|=\dfrac{3+10}{6}\)

\(\Leftrightarrow\left|\dfrac{1}{2}-x\right|=\dfrac{13}{6}\)

Xét trường hợp 1: \(\dfrac{1}{2}-x=\dfrac{13}{6}\)

\(\Rightarrow x=\dfrac{1}{2}-\dfrac{13}{6}\)

\(\Rightarrow x=\dfrac{3}{6}-\dfrac{13}{6}\)

\(\Rightarrow x=\dfrac{3-13}{6}\)

\(\Rightarrow x=\dfrac{-10}{6}\)

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

Xét trường hợp 2: \(\dfrac{1}{2}-x=\dfrac{-13}{6}\)

\(\Rightarrow x=\dfrac{1}{2}-\dfrac{-13}{6}\)

\(\Rightarrow x=\dfrac{1}{2}+\dfrac{13}{6}\)

\(\Rightarrow x=\dfrac{3}{6}+\dfrac{13}{6}\)

\(\Rightarrow x=\dfrac{3+13}{6}\)

\(\Rightarrow x=\dfrac{16}{6}\)

\(\Rightarrow x=\dfrac{8}{3}\)

Vậy \(x=\dfrac{-5}{3}\) hoặc \(x=\dfrac{8}{3}\)

Answer 2

\(\left|\dfrac{1}{2}-x\right|\) - 1\(\dfrac{2}{3}\)= 0.5

=> \(\left|\dfrac{1}{2}-x\right|\) = 0.5 + 1\(\dfrac{2}{3}\)

=>> \(\left|\dfrac{1}{2}-x\right|\) =\(\dfrac{13}{6}\)

=> \(\left[{}\begin{matrix}\dfrac{1}{2}-x=\dfrac{13}{6}\\\dfrac{1}{2}-x=\dfrac{-13}{6}\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}x=\dfrac{-5}{3}\\x=\dfrac{8}{3}\end{matrix}\right.\)

Chúc bạn học tốt !

Answer 3

\(\left|\dfrac{1}{2}-x\right|-1\dfrac{2}{3}=0,5\)

=>\(\left|\dfrac{1}{2}-x\right|-\dfrac{5}{3}=\dfrac{1}{2}\)

=> \(\left|\dfrac{1}{2}-x\right|=\dfrac{13}{6}\)

TH1 \(\dfrac{1}{2}-x=\dfrac{13}{6}\)

=> x=-\(\dfrac{5}{3}\)

TH2 \(\dfrac{1}{2}-x=-\dfrac{13}{6}\)

=> x=\(\dfrac{8}{3}\)

vậy x=-\(\dfrac{5}{3}\)hoặc x= \(\dfrac{8}{3}\)