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1) \(x-\left|1\frac{1}{6}\right|=\frac{5}{21}\)
\(\Rightarrow x-\frac{5}{21}=\left|1\frac{1}{6}\right|\)
\(\Rightarrow x-\frac{5}{21}=\frac{7}{6}\)
\(\Rightarrow x=\frac{7}{6}+\frac{5}{21}=\frac{49}{42}+\frac{10}{42}=\frac{59}{42}\)
2) \(x+\left|-1\frac{2}{3}\right|=\left|-\frac{3}{4}\right|\)
\(\Rightarrow x+\left|-1\frac{2}{3}\right|=\frac{3}{4}\)
\(\Rightarrow x-\frac{3}{4}=-\left|-1\frac{2}{3}\right|\)
\(\Rightarrow x-\frac{3}{4}=-1\frac{2}{3}\)
\(\Rightarrow x-\frac{3}{4}=-\frac{5}{3}\)
\(\Rightarrow x=-\frac{5}{3}+\frac{3}{4}=-\frac{11}{12}\)
3) \(\left|x-\frac{1}{3}\right|=\frac{5}{2}\)
\(\Rightarrow\left[{}\begin{matrix}x-\frac{1}{3}=\frac{5}{2}\\x-\frac{1}{3}=-\frac{5}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{5}{2}+\frac{1}{3}=\frac{17}{6}\\x=-\frac{5}{2}+\frac{1}{3}=-\frac{13}{6}\end{matrix}\right.\)
4) \(\left|x+\frac{2}{3}\right|=0\)
\(\Rightarrow x+\frac{2}{3}=0\)
\(\Rightarrow x=0-\frac{2}{3}=-\frac{2}{3}\)
5) \(\left|x+2\right|=\frac{1}{3}-\frac{1}{5}\)
\(\Rightarrow\left|x+2\right|=\frac{2}{15}\)
\(\Rightarrow\left[{}\begin{matrix}x+2=\frac{2}{15}\\x+2=-\frac{2}{15}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{2}{15}-2=-\frac{28}{15}\\x=-\frac{2}{15}-2=-\frac{32}{15}\end{matrix}\right.\)
6) \(\left|x-4\right|=\frac{1}{5}-\left(\frac{1}{2}-\frac{5}{4}\right)\)
\(\Rightarrow\left|x-4\right|=\frac{19}{20}\)
\(\Rightarrow\left[{}\begin{matrix}x-4=\frac{19}{20}\\x-4=-\frac{19}{20}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{19}{20}+4=\frac{99}{20}\\x=-\frac{19}{20}+4=\frac{61}{20}\end{matrix}\right.\)
7) \(\left|x-\frac{5}{4}\right|=-\frac{1}{3}\)
Vì \(\left|x-\frac{5}{4}\right|\ge0\)
=> Không có giá trị x thỏa mãn với điều kiện trên
1) \(\frac{4}{7}-\frac{1}{14}+\left|\frac{-5}{21}\right|\)
\(=\frac{4}{7}-\frac{1}{14}+\frac{5}{21}\)
\(=\frac{24}{42}-\frac{3}{42}+\frac{10}{42}\)
\(=\frac{31}{42}\)
2) \(\left|\frac{-2}{3}\right|-\frac{1}{2}+3\)
\(=\frac{2}{3}-\frac{1}{2}+\frac{3}{1}\)
\(=\frac{4}{6}-\frac{3}{6}+\frac{18}{6}\)
\(=\frac{19}{6}\)
3) \(\left|\frac{7}{-4}\right|-\frac{5}{8}+\frac{-2}{3}\)
\(=\frac{7}{4}-\frac{5}{8}+\frac{-2}{3}\)
\(=\frac{42}{24}-\frac{15}{24}+\frac{-16}{24}\)
\(=\frac{11}{24}\)
4) \(\frac{4}{5}+\left|\frac{-3}{2}\right|+\frac{1}{-4}\)
\(=\frac{4}{5}+\frac{3}{2}+\frac{-1}{4}\)
\(=\frac{16}{20}+\frac{30}{20}+\frac{-5}{20}\)
\(=\frac{41}{20}\)
5) \(\left|\frac{-1}{4}\right|-3+\frac{3}{4}\)
\(=\frac{1}{4}-\frac{3}{1}+\frac{3}{4}\)
\(=\frac{1}{4}-\frac{12}{4}+\frac{3}{4}\)
\(=-2\)
6) \(\left|\frac{-1}{3}\right|-\frac{5}{4}+\frac{1}{5}\)
\(=\frac{1}{3}-\frac{5}{4}+\frac{1}{5}\)
\(=\frac{20}{60}-\frac{75}{60}+\frac{12}{60}\)
\(=\frac{-43}{60}\)