\(a,\left|2x-5\right|=4\)
\(\Rightarrow\left\{{}\begin{matrix}\left|2x-5\right|=4\\\left|2x-5\right|=-4\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}2x=4+5\\2x=-4+5\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}2x=9\\2x=1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=9:2\\x=1:2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{9}{2}\\x=\dfrac{1}{2}\end{matrix}\right.\)
\(b,\dfrac{1}{3}-\left|\dfrac{5}{4}-2x\right|=\dfrac{1}{4}\)
\(\Rightarrow\) \(\left|\dfrac{5}{4}-2x\right|=\dfrac{1}{3}-\dfrac{1}{4}\)
\(\Rightarrow\) \(\left|\dfrac{5}{4}-2x\right|=\dfrac{1}{12}\)
\(\Rightarrow\left\{{}\begin{matrix}\left|\dfrac{5}{4}-2x\right|=\dfrac{1}{12}\\\left|\dfrac{5}{4}-2x\right|=-\dfrac{1}{12}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}2x=\dfrac{5}{4}-\dfrac{1}{12}\\2x=\dfrac{5}{4}-\left(-\dfrac{1}{12}\right)\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}2x=\dfrac{7}{6}\\2x=\dfrac{4}{3}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{7}{6}:2\\x=\dfrac{4}{3}:2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{7}{12}\\x=\dfrac{2}{3}\end{matrix}\right.\)
\(c,\dfrac{1}{2}-\left|x+\dfrac{1}{5}\right|=\dfrac{1}{3}\)
\(\Rightarrow\left|x+\dfrac{1}{5}\right|=\dfrac{1}{2}-\dfrac{1}{3}\)
\(\Rightarrow\left|x+\dfrac{1}{5}\right|=\dfrac{1}{6}\)
\(\Rightarrow\left\{{}\begin{matrix}x+\dfrac{1}{5}=\dfrac{1}{6}\\x+\dfrac{1}{5}=-\dfrac{1}{6}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{1}{6}-\dfrac{1}{5}\\x=-\dfrac{1}{6}-\dfrac{1}{5}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{-1}{30}\\x=\dfrac{-11}{30}\end{matrix}\right.\)
\(d,\dfrac{3}{4}-\left|2x+1\right|=\dfrac{7}{8}\)
\(\Rightarrow2x+1=\dfrac{3}{4}-\dfrac{7}{8}\)
\(\Rightarrow2x+1=\dfrac{-1}{8}\)
\(\Rightarrow\left\{{}\begin{matrix}2x+1=\dfrac{-1}{8}\\2x+1=\dfrac{1}{8}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}2x=\dfrac{-1}{8}-1\\2x=\dfrac{1}{8}-1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}2x=\dfrac{-9}{8}\\2x=\dfrac{-7}{8}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{-9}{8}:2\\x=\dfrac{-7}{8}:2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{-1}{2}\\x=\dfrac{-7}{16}\end{matrix}\right.\)
a: =>2x-5=4 hoặc 2x-5=-4
=>2x=9 hoặc 2x=1
=>x=9/2 hoặc x=1/2
b: =>|2x-5/4|=1/12
=>2x-5/4=1/12 hoặc 2x-5/4=-1/12
=>2x=4/3 hoặc 2x=7/6
=>x=2/3 hoặc x=7/12
c: =>|x+1/5|=1/6
=>x+1/5=1/6 hoặc x+1/5=-1/6
=>x=-1/30 hoặc x=-11/30
