Giải:
5) \(\left(2x+\dfrac{3}{5}\right)^2-\dfrac{9}{25}=0\)
\(\left(2x+\dfrac{3}{5}\right)^2=0+\dfrac{9}{25}\)
\(\left(2x+\dfrac{3}{5}\right)^2=\dfrac{9}{25}\)
\(\Rightarrow\left[{}\begin{matrix}\left(2x+\dfrac{3}{5}\right)^2=\left(\dfrac{3}{5}\right)^2\\\left(2x+\dfrac{3}{5}\right)^2=\left(\dfrac{-3}{5}\right)^2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x+\dfrac{3}{5}=\dfrac{3}{5}\\2x+\dfrac{3}{5}=\dfrac{-3}{5}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{-3}{5}\end{matrix}\right.\)
6) \(\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|-\dfrac{3}{2}=\dfrac{1}{4}\)
\(\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|=\dfrac{1}{4}+\dfrac{3}{2}\)
\(\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|=\dfrac{7}{4}\)
\(\Rightarrow\left[{}\begin{matrix}\dfrac{1}{2}x-\dfrac{1}{3}=\dfrac{7}{4}\\\dfrac{1}{2}x-\dfrac{1}{3}=\dfrac{-7}{4}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{25}{6}\\x=\dfrac{-17}{6}\end{matrix}\right.\)
7) \(3.\left(x-\dfrac{1}{2}\right)-5.\left(x+\dfrac{3}{5}\right)=-x+\dfrac{1}{5}\)
\(\Rightarrow3x-\dfrac{3}{2}-5x-3=-x+\dfrac{1}{5}\)
\(\Rightarrow3x-5x+x=\dfrac{1}{5}+\dfrac{3}{2}+3\)
\(\Rightarrow-x=\dfrac{47}{10}\)
\(\Rightarrow x=\dfrac{-47}{10}\)
8) \(\left|2\dfrac{2}{9}-x\right|=\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}\)
\(\left|\dfrac{20}{9}-x\right|=\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}\)
\(\left|\dfrac{20}{9}-x\right|=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}\)
\(\left|\dfrac{20}{9}-x\right|=\dfrac{1}{3}-\dfrac{1}{9}\)
\(\left|\dfrac{20}{9}-x\right|=\dfrac{2}{9}\)
\(\Rightarrow\left[{}\begin{matrix}\dfrac{20}{9}-x=\dfrac{2}{9}\\\dfrac{20}{9}-x=\dfrac{-2}{9}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{22}{9}\end{matrix}\right.\)
9) \(x.\left(\dfrac{8888}{1212}+\dfrac{8888}{2020}+\dfrac{8888}{3030}+\dfrac{8888}{4242}+\dfrac{8888}{5656}\right)=-5\)
\(\Rightarrow x.\left(\dfrac{88}{12}+\dfrac{88}{20}+\dfrac{88}{30}+\dfrac{88}{42}+\dfrac{88}{56}\right)=-5\)
\(\Rightarrow x.88.\left(\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}\right)=-5\)
\(\Rightarrow x.88.\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}\right)=-5\)
\(\Rightarrow x.88.\left(\dfrac{1}{3}-\dfrac{1}{8}\right)=-5\)
\(\Rightarrow x.88.\dfrac{5}{24}=-5\)
\(\Rightarrow x.\dfrac{55}{3}=-5\)
\(\Rightarrow x=-5:\dfrac{55}{3}\)
\(\Rightarrow x=\dfrac{-3}{11}\)
10) \(\dfrac{2}{3}x-70\dfrac{10}{11}:\left(\dfrac{131313}{151515}+\dfrac{131313}{353535}+\dfrac{131313}{636363}+\dfrac{131313}{999999}\right)=-5\)
\(\Rightarrow\dfrac{2}{3}x-\dfrac{780}{11}:\left(\dfrac{13}{15}+\dfrac{13}{35}+\dfrac{13}{63}+\dfrac{13}{99}\right)=-5\)
\(\Rightarrow\dfrac{2}{3}x-\dfrac{780}{11}:\left[13.\left(\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}+\dfrac{1}{9.11}\right)\right]=-5\)
\(\Rightarrow\dfrac{2}{3}x-\dfrac{780}{11}:\left[13.\dfrac{1}{2}.\left(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}\right)\right]=-5\)
\(\Rightarrow\dfrac{2}{3}x-\dfrac{780}{11}:\left[\dfrac{13}{2}.\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}\right)\right]=-5\)
\(\Rightarrow\dfrac{2}{3}x-\dfrac{780}{11}:\left[\dfrac{13}{2}.\left(\dfrac{1}{3}-\dfrac{1}{11}\right)\right]=-5\)
\(\Rightarrow\dfrac{2}{3}x-\dfrac{780}{11}:\left[\dfrac{13}{2}.\dfrac{8}{33}\right]=-5\)
\(\Rightarrow\dfrac{2}{3}x-\dfrac{780}{11}:\dfrac{52}{33}=-5\)
\(\Rightarrow\dfrac{2}{3}x-45=-5\)
\(\Rightarrow\dfrac{2}{3}x=-5+45\)
\(\Rightarrow\dfrac{2}{3}x=40\)
\(\Rightarrow x=40:\dfrac{2}{3}\)
\(\Rightarrow x=60\)
Chúc bạn học tốt!
