Bài 1:

a) \(\dfrac{2}{5}\cdot x-\dfrac{1}{4}=\dfrac{1}{10}\)

\(\dfrac{2}{5}\cdot x=\dfrac{1}{10}+\dfrac{1}{4}\)

\(\dfrac{2}{5}\cdot x=\dfrac{7}{20}\)

\(x=\dfrac{7}{20}:\dfrac{2}{5}\)

\(x=\dfrac{7}{8}\)

Vậy \(x=\dfrac{7}{8}\).

b) \(\dfrac{3}{5}=\dfrac{24}{x}\)

\(x=\dfrac{5\cdot24}{3}\)

\(x=40\)

Vậy \(x=40\).

c) \(\left(2x-3\right)^2=16\)

\(\left(2x-3\right)^2=4^2\)

\(\circledast\)TH₁: \(2x-3=4\\ 2x=4+3\\ 2x=7\\ x=\dfrac{7}{2}\)

\(\circledast\)TH₂: \(2x-3=-4\\ 2x=-4+3\\ 2x=-1\\ x=\dfrac{-1}{2}\)

Vậy \(x\in\left\{\dfrac{7}{2};\dfrac{-1}{2}\right\}\).

Bài 2:

a) \(25\%-4\dfrac{2}{5}+0.3:\dfrac{6}{5}\)

\(=\dfrac{1}{4}-\dfrac{22}{5}+\dfrac{3}{10}:\dfrac{6}{5}\)

\(=\dfrac{1}{4}-\dfrac{22}{5}+\dfrac{3}{10}\cdot\dfrac{5}{6}\)

\(=\dfrac{1}{4}-\dfrac{22}{5}+\dfrac{1}{4}\)

\(=\dfrac{5}{20}-\dfrac{88}{20}+\dfrac{5}{20}\)

\(=\dfrac{5-88+5}{20}\)

\(=\dfrac{78}{20}=\dfrac{39}{10}\)

b) \(\left(\dfrac{1}{6}-\dfrac{1}{5^2}\cdot5+\dfrac{1}{30}\right)\left(\dfrac{2011}{2010}+\dfrac{2010}{1009}+\dfrac{2009}{2008}\right)\)

\(=\left(\dfrac{1}{6}-\dfrac{1}{25}\cdot5+\dfrac{1}{30}\right)\left(\dfrac{2011}{2010}+\dfrac{2010}{1009}+\dfrac{2009}{2008}\right)\)

\(=\left(\dfrac{1}{6}-\dfrac{1}{5}+\dfrac{1}{30}\right)\left(\dfrac{2011}{2010}+\dfrac{2010}{1009}+\dfrac{2009}{2008}\right)\)

\(=\left(\dfrac{5}{30}-\dfrac{6}{30}+\dfrac{1}{30}\right)\left(\dfrac{2011}{2010}+\dfrac{2010}{1009}+\dfrac{2009}{2008}\right)\)

\(=\left(\dfrac{5-6+1}{30}\right)\left(\dfrac{2011}{2010}+\dfrac{2010}{1009}+\dfrac{2009}{2008}\right)\)

\(=0\cdot\left(\dfrac{2011}{2010}+\dfrac{2010}{1009}+\dfrac{2009}{2008}\right)\)

\(=0\)

Bài 3:

a) \(\dfrac{4}{19}\cdot\dfrac{-3}{7}+\dfrac{-3}{7}\cdot\dfrac{15}{19}\)

\(=\dfrac{-3}{7}\left(\dfrac{4}{19}+\dfrac{15}{19}\right)\)

\(=\dfrac{-3}{7}\cdot1\)

\(=\dfrac{-3}{7}\)

b) \(7\dfrac{5}{9}-\left(2\dfrac{3}{4}+3\dfrac{5}{9}\right)\)

\(=\dfrac{68}{9}-\dfrac{11}{4}-\dfrac{32}{9}\)

\(=\dfrac{68}{9}-\dfrac{32}{9}-\dfrac{11}{4}\)

\(=4-\dfrac{11}{4}\)

\(=\dfrac{16}{4}-\dfrac{11}{4}\)

\(\dfrac{5}{4}\)

Bài 4:

\(\dfrac{4}{12\cdot14}+\dfrac{4}{14\cdot16}+\dfrac{4}{16\cdot18}+...+\dfrac{4}{58\cdot60}\)

\(=2\left(\dfrac{1}{12\cdot14}+\dfrac{1}{14\cdot16}+\dfrac{1}{16\cdot18}+...+\dfrac{1}{58\cdot60}\right)\)

\(=2\left(\dfrac{1}{12}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{18}+...+\dfrac{1}{58}-\dfrac{1}{60}\right)\)

\(=2\left(\dfrac{1}{12}-\dfrac{1}{60}\right)\)

\(=2\left(\dfrac{5}{60}-\dfrac{1}{60}\right)\)

\(=2\cdot\dfrac{1}{15}\)

\(=\dfrac{2}{15}\)

a.\(\dfrac{-4}{5}-\left(\dfrac{2}{3}x+1\dfrac{1}{4}\right)=\dfrac{2}{7}\)

\(\left(\dfrac{2}{3}x+1\dfrac{1}{4}\right)=\dfrac{-4}{5}-\dfrac{2}{7}=\dfrac{-38}{35}\)

\(\dfrac{2}{3}x=\dfrac{-38}{35}-1\dfrac{1}{4}\)

\(\dfrac{2}{3}x=\dfrac{-327}{140}\Rightarrow x=\dfrac{-327}{140}:\dfrac{2}{3}=\dfrac{-981}{280}\)

Vậy \(x=\dfrac{-981}{280}\)

b. \(\dfrac{5}{6}+\left(\dfrac{3}{4}-\dfrac{1}{2}:x\right)=\dfrac{-2}{3}\)

\(\left(\dfrac{3}{4}-\dfrac{1}{2}:x\right)=\dfrac{-2}{3}-\dfrac{5}{6}=\dfrac{-3}{2}\)

\(\dfrac{1}{2}:x=\dfrac{3}{4}-\dfrac{-3}{2}\)

\(\dfrac{1}{2}:x=\dfrac{9}{4}\Rightarrow x=\dfrac{1}{2}:\dfrac{9}{4}=\dfrac{2}{9}\)

Vậy \(x=\dfrac{2}{9}\)

c. \(\left(\dfrac{4}{5}x-1\dfrac{1}{3}\right):\dfrac{3}{4}=0,7\)

\(\left(\dfrac{4}{5}x-1\dfrac{1}{3}\right)=0,7.\dfrac{3}{4}=\dfrac{21}{40}\)

\(\dfrac{4}{5}x=\dfrac{21}{40}+1\dfrac{1}{3}=\dfrac{223}{120}\)

\(\Rightarrow x=\dfrac{223}{120}:\dfrac{4}{5}=\dfrac{223}{96}\)

Vậy \(x=\dfrac{223}{96}\)

d. \(\dfrac{5}{6}-\dfrac{3}{4}x=1\dfrac{1}{3}+0,5x\)

\(0,5x+\dfrac{3}{4}x=\dfrac{5}{6}-1\dfrac{1}{3}\)

\(\dfrac{5}{4}x=\dfrac{-1}{2}\Rightarrow x=\dfrac{-1}{2}:\dfrac{5}{4}=\dfrac{-2}{5}\)

Vậy \(x=\dfrac{-2}{5}\)

a) x.(\(\dfrac{6}{7}\)+\(\dfrac{5}{6}\))=\(\dfrac{3}{4}\)

x.\(\dfrac{71}{42}\)=\(\dfrac{3}{4}\)

x=\(\dfrac{3}{4}\):\(\dfrac{71}{42}\)

x=\(\dfrac{63}{142}\)

a.\(\dfrac{6}{7}x+\dfrac{5}{6}x=\dfrac{3}{4}\)

\(x.\left(\dfrac{6}{7}+\dfrac{5}{6}\right)=\dfrac{3}{4}\)

\(x.\dfrac{71}{42}=\dfrac{3}{4}\)

\(x=\dfrac{3}{4}:\dfrac{71}{42}\)

\(x=\dfrac{63}{142}\)

b\(\dfrac{5}{4}-\dfrac{3}{5}:x=1\dfrac{1}{3}\)

\(\dfrac{3}{5}:x=\dfrac{5}{4}-1\dfrac{1}{3}\)

\(\dfrac{3}{5}:x=\dfrac{-1}{12}\)

\(x=\dfrac{3}{5}:\dfrac{-1}{12}\)

\(x=\dfrac{-36}{5}\)

c. \(\left(\dfrac{4}{7}x-\dfrac{1}{3}\right):3\dfrac{1}{2}=0,5\)

\(\left(\dfrac{4}{7}x-\dfrac{1}{3}\right)=0,5:3\dfrac{1}{2}\)

\(\dfrac{4}{7}x-\dfrac{1}{3}=\dfrac{1}{7}\)

\(\dfrac{4}{7}x=\dfrac{1}{7}+\dfrac{1}{3}\)

\(\dfrac{4}{7}x=\dfrac{10}{21}\)

\(x=\dfrac{10}{21}:\dfrac{4}{7}\)

\(x=\dfrac{5}{6}\)

d.\(\dfrac{4}{5}-\dfrac{2}{3}x=1\dfrac{1}{4}+2,5x\)

\(\dfrac{4}{5}-\left(\dfrac{2}{3}x-2,5x\right)=1\dfrac{1}{4}\)

\(\dfrac{4}{5}-\dfrac{-11}{6}x=1\dfrac{1}{4}\)

\(\dfrac{-11}{6}x=\dfrac{4}{5}-1\dfrac{1}{4}\)

\(\dfrac{-11}{6}x=\dfrac{-9}{20}\)

\(x=\dfrac{-9}{20}:\dfrac{-11}{6}\)

\(x=\dfrac{27}{110}\)

có sai sót j xin bn thông cảm !

a)\(\dfrac{2}{3}x-\dfrac{5}{6}=1\dfrac{1}{4}\)

\(\dfrac{2}{3}x-\dfrac{5}{6}=\dfrac{5}{4}\)

\(\dfrac{2}{3}x=\dfrac{5}{4}+\dfrac{5}{6}\)

\(\dfrac{2}{3}x=\dfrac{25}{12}\)

\(x=\dfrac{25}{12}:\dfrac{2}{3}\)

=>\(x=\dfrac{25}{8}\)

a) \(\dfrac{2}{3}x-\dfrac{5}{6}=1\dfrac{1}{4}\) b) \(2\dfrac{1}{3}-\dfrac{4}{5}:x=0,2\)

\(\dfrac{2}{3}x-\dfrac{5}{6}=\dfrac{5}{4}\) \(\dfrac{7}{3}-\dfrac{4}{5}:x=\dfrac{1}{5}\)

\(\dfrac{2}{3}x=\dfrac{5}{4}-\dfrac{5}{6}\) \(\dfrac{4}{5}:x=\dfrac{7}{3}-\dfrac{1}{5}\)

\(\dfrac{2}{3}x=\dfrac{30}{24}-\dfrac{20}{24}\) \(\dfrac{4}{5}:x=\dfrac{35}{15}-\dfrac{3}{15}\)

\(\dfrac{2}{3}x=\dfrac{5}{12}\) \(\dfrac{4}{5}:x=\dfrac{32}{15}\)

\(x=\dfrac{5}{12}:\dfrac{2}{3}\) \(x=\dfrac{4}{5}:\dfrac{32}{15}\)

\(x=\dfrac{5}{12}:\dfrac{8}{12}\) \(x=\dfrac{4}{5}.\dfrac{15}{32}\)

\(x=\dfrac{5}{12}.\dfrac{12}{8}=\dfrac{5}{8}\) \(x=\dfrac{4.15}{5.32}\)

\(x=\dfrac{1.3}{1.8}=\dfrac{3}{8}\)

d)\(\left(\dfrac{4}{3}-\dfrac{1}{4}x\right)^3=\dfrac{-8}{27}\)

\(\left(\dfrac{4}{3}-\dfrac{1}{4}x\right)^3=\left(\dfrac{-2}{3}\right)^3\)

\(\Rightarrow\dfrac{4}{3}-\dfrac{1}{4}x=\dfrac{-2}{3}\)

\(\Rightarrow\dfrac{1}{4}x=\dfrac{4}{3}-\dfrac{-2}{3}\)

\(\Rightarrow\dfrac{1}{4}x=2\)

\(\Rightarrow x=2:\dfrac{1}{4}\)

\(\Rightarrow x=2.4=8\)

tìm x a)
\(\dfrac{7}{2}\)-\(\left(x+\dfrac{7}{10}\right)\): \(\dfrac{6}{5}\) = \(\dfrac{-5}{4}\)
\(\left(x+\dfrac{7}{10}\right)\): \(\dfrac{6}{5}\) = \(\dfrac{-5}{4}\) + \(\dfrac{7}{2}\)
\(\left(x+\dfrac{7}{10}\right)\): \(\dfrac{6}{5}\) = \(\dfrac{-5}{12}+\dfrac{7}{12}\)
\(\left(x+\dfrac{7}{10}\right)\): \(\dfrac{6}{5}\) = \(\dfrac{-12}{12}=1\)
\(x+\dfrac{7}{10}\)= 1 . \(\dfrac{6}{5}\)
*Rồi tự làm phần tt đi

Mình ghi kết quả luôn nha bạn

a/ \(\dfrac{5}{6}-\left(\dfrac{3}{6}x-\dfrac{1}{5}\right)=\dfrac{-5}{12}\)

\(\Leftrightarrow\dfrac{1}{2}x-\dfrac{1}{5}=\dfrac{5}{6}-\dfrac{-5}{12}\)

\(\Leftrightarrow\dfrac{1}{2}x-\dfrac{1}{5}=\dfrac{5}{4}\)

\(\Leftrightarrow\dfrac{1}{2}x=\dfrac{29}{20}\)

\(\Leftrightarrow x=\dfrac{29}{10}\)

Vậy ...

b/ \(\left(4x-3\right)\left(\dfrac{5}{4}x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}4x-3=0\\\dfrac{5}{4}x+2=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}4x=3\\\dfrac{5}{4}x=-2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{4}\\x=-\dfrac{8}{5}\end{matrix}\right.\)

Vậy .....

c/ \(\left|\dfrac{7}{8}x-\dfrac{2}{3}\right|-\dfrac{3}{4}=1,5\)

\(\Leftrightarrow\left|\dfrac{7}{8}x-\dfrac{2}{3}\right|=\dfrac{9}{4}\)

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{7}{8}x-\dfrac{2}{3}=\dfrac{9}{4}\\\dfrac{7}{8}x-\dfrac{2}{3}=-\dfrac{9}{4}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{7}{8}x=\dfrac{35}{12}\\\dfrac{7}{8}x=-\dfrac{19}{12}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{10}{3}\\x=-\dfrac{38}{21}\end{matrix}\right.\)

Vậy ......

d/ \(\left(\dfrac{3}{5}x-\dfrac{1}{2}\right)^3=\dfrac{8}{125}\)

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

\(\Leftrightarrow\dfrac{3}{5}x-\dfrac{1}{2}=\dfrac{2}{5}\)

\(\Leftrightarrow\dfrac{3}{5}x=\dfrac{9}{10}\)

\(\Leftrightarrow x=\dfrac{3}{2}\)

Vậy ...

a. \(\dfrac{5}{6}-\left(\dfrac{3}{6}x-\dfrac{1}{5}\right)=\dfrac{-5}{12}\)

\(\left(\dfrac{3}{6}x-\dfrac{1}{5}\right)=\dfrac{5}{6}-\dfrac{-5}{12}\)

\(\left(\dfrac{3}{6}x-\dfrac{1}{5}\right)=\dfrac{5}{4}\)

\(\dfrac{3}{6}x=\dfrac{5}{4}+\dfrac{1}{5}\)

\(\dfrac{3}{6}x=\dfrac{29}{20}\)

\(x=\dfrac{29}{20}:\dfrac{3}{6}\)

\(x=\dfrac{29}{10}\)

Vậy...

b. \(\left(4x-3\right).\left(\dfrac{5}{4}x+2\right)=0\)

\(\left[{}\begin{matrix}4x-3=0\\\dfrac{5}{4}x+2=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}4x=3\\\dfrac{5}{4}x=-2\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{4}\\x=\dfrac{-8}{5}\end{matrix}\right.\)

Vậy ...

c. \(\left|\dfrac{7}{8}x-\dfrac{2}{3}\right|-\dfrac{3}{4}=1,5\)

\(\left|\dfrac{7}{8}x-\dfrac{2}{3}\right|=1,5+\dfrac{3}{4}\)

\(\left|\dfrac{7}{8}x-\dfrac{2}{3}\right|=\dfrac{9}{4}\)

\(\Rightarrow\left[{}\begin{matrix}\dfrac{7}{8}x-\dfrac{2}{3}=\dfrac{9}{4}\\\dfrac{7}{8}x-\dfrac{2}{3}=\dfrac{-9}{4}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\dfrac{7}{8}x=\dfrac{35}{12}\\\dfrac{7}{8}x=\dfrac{-19}{12}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\dfrac{10}{3}\\x=\dfrac{-38}{21}\end{matrix}\right.\)

Vậy...

3) \(\left(x+\dfrac{1}{5}\right)^2\) + \(\dfrac{17}{25}\) = \(\dfrac{26}{25}\)

=> \(\left(x+\dfrac{1}{5}\right)^2\) = \(\dfrac{26}{25}\) - \(\dfrac{17}{25}\)

=> \(\left(x+\dfrac{1}{5}\right)^2\) = \(\dfrac{9}{25}\)

=> \(\left(x+\dfrac{1}{5}\right)^2\) = \(\dfrac{3}{5}.\dfrac{3}{5}\)

=> \(\left(x+\dfrac{1}{5}\right)^2\) = \(\left(\dfrac{3}{5}\right)^2\)

=> \(x\) + \(\dfrac{1}{5}\) = \(\dfrac{3}{5}\)

=> \(x\) = \(\dfrac{3}{5}\) - \(\dfrac{1}{5}\)

=> \(x\) = \(\dfrac{2}{5}\)

4) -1\(\dfrac{5}{27}\) - \(\left(3x-\dfrac{7}{9}\right)^3\) = \(\dfrac{-24}{27}\)

=> \(\dfrac{-32}{27}\) - \(\left(3x-\dfrac{7}{9}\right)^3\) = \(\dfrac{-8}{9}\)

=> \(\left(3x-\dfrac{7}{9}\right)^3\) = \(\dfrac{-32}{27}\) - \(\dfrac{-8}{9}\)

=> \(\left(3x-\dfrac{7}{9}\right)^3\) = \(\dfrac{-8}{27}\)

=> \(\left(3x-\dfrac{7}{9}\right)^3\) = \(\dfrac{-2}{3}\) . \(\dfrac{-2}{3}\) . \(\dfrac{-2}{3}\)

=> \(\left(3x-\dfrac{7}{9}\right)^3\) = \(\left(\dfrac{-2}{3}\right)^3\)

=> \(3x-\dfrac{7}{9}=\dfrac{-2}{3}\)

=> \(3x=\dfrac{-2}{3}+\dfrac{7}{9}\)

=> \(3x=\dfrac{1}{9}\)

=> \(x=\dfrac{1}{9}:3\)

=> \(x=\dfrac{1}{27}\)

giúp mk với