a: |x|=5,6
=>\(\left[{}\begin{matrix}x=5,6\\x=-5,6\end{matrix}\right.\)
c: \(\left|x\right|=3\dfrac{1}{5}\)
=>\(\left|x\right|=3,2\)
=>\(\left[{}\begin{matrix}x=3,2\\x=-3,2\end{matrix}\right.\)
d: |x|=-2,1
mà -2,1<0
nên \(x\in\varnothing\)
d: |x-3,5|=5
=>\(\left[{}\begin{matrix}x-3,5=5\\x-3,5=-5\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=8,5\\x=-1,5\end{matrix}\right.\)
e: \(\left|x+\dfrac{3}{4}\right|-\dfrac{1}{2}=0\)
=>\(\left|x+\dfrac{3}{4}\right|=\dfrac{1}{2}\)
=>\(\left[{}\begin{matrix}x+\dfrac{3}{4}=\dfrac{1}{2}\\x+\dfrac{3}{4}=-\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{4}\\x=-\dfrac{5}{4}\end{matrix}\right.\)
f: \(\left|4x\right|-\left|-13,5\right|=\left|2\dfrac{1}{4}\right|\)
=>\(4\left|x\right|=2,25+13,5=15,75\)
=>\(\left|x\right|=\dfrac{63}{16}\)
=>\(x=\pm\dfrac{63}{16}\)
g: \(\dfrac{5}{6}-\left|2-x\right|=\dfrac{1}{3}\)
=>\(\dfrac{5}{6}-\left|x-2\right|=\dfrac{1}{3}\)
=>\(\left|x-2\right|=\dfrac{5}{6}-\dfrac{1}{3}=\dfrac{1}{2}\)
=>\(\left[{}\begin{matrix}x-2=\dfrac{1}{2}\\x-2=-\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=\dfrac{3}{2}\end{matrix}\right.\)
h: \(\left|x-\dfrac{2}{5}\right|+\dfrac{1}{2}=\dfrac{3}{4}\)
=>\(\left|x-\dfrac{2}{5}\right|=\dfrac{3}{4}-\dfrac{1}{2}=\dfrac{1}{4}\)
=>\(\left[{}\begin{matrix}x-\dfrac{2}{5}=\dfrac{1}{4}\\x-\dfrac{2}{5}=-\dfrac{1}{4}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{4}+\dfrac{2}{5}=\dfrac{13}{20}\\x=-\dfrac{1}{4}+\dfrac{2}{5}=\dfrac{-5+8}{20}=\dfrac{3}{20}\end{matrix}\right.\)
i: \(\left|5-3x\right|+\dfrac{2}{3}=\dfrac{1}{6}\)
=>\(\left|3x-5\right|=\dfrac{1}{6}-\dfrac{2}{3}=\dfrac{1}{6}-\dfrac{4}{6}=-\dfrac{3}{6}=-\dfrac{1}{2}< 0\)
=>\(x\in\varnothing\)
k: \(-2,5+\left|3x+5\right|=-1,5\)
=>|3x+5|=-1,5+2,5=1
=>\(\left[{}\begin{matrix}3x+5=1\\3x+5=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=-4\\3x=-6\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=-\dfrac{4}{3}\\x=-2\end{matrix}\right.\)
m: \(\dfrac{1}{5}-\left|\dfrac{1}{5}-x\right|=\dfrac{1}{5}\)
=>\(\left|\dfrac{1}{5}-x\right|=\dfrac{1}{5}-\dfrac{1}{5}=0\)
=>\(\dfrac{1}{5}-x=0\)
=>\(x=\dfrac{1}{5}\)
n: \(-\dfrac{22}{15}x+\dfrac{1}{3}=\left|-\dfrac{2}{3}+\dfrac{1}{5}\right|\)
=>\(-\dfrac{22}{15}x+\dfrac{1}{3}=\dfrac{2}{3}-\dfrac{1}{5}\)
=>\(-\dfrac{22}{15}x=\dfrac{1}{3}-\dfrac{1}{5}=\dfrac{2}{15}\)
=>-22x=2
=>\(x=-\dfrac{1}{11}\)
