a) Ta có: \(\left(x-2\right)^3+\frac{8}{27}=0\)

\(\Leftrightarrow\left(x-2\right)^3=\frac{-8}{27}\)

\(\Leftrightarrow\left(x-2\right)^3=\left(-\frac{2}{3}\right)^3\)

\(\Leftrightarrow x-2=\frac{-2}{3}\)

hay \(x=\frac{-2}{3}+2=\frac{4}{3}\)

Vậy: \(x=\frac{4}{3}\)

b) Ta có: \(4\frac{1}{3}:\frac{x}{4}=6:0,3\)

\(\Leftrightarrow\frac{13}{3}\cdot\frac{4}{x}=20\)

\(\Leftrightarrow\frac{4}{x}=20:\frac{13}{3}=20\cdot\frac{3}{13}=\frac{60}{13}\)

hay \(x=\frac{13\cdot4}{60}=\frac{13}{15}\)

Vậy: \(x=\frac{13}{15}\)

c) Ta có: \(\left(0,25-30\%x\right)\cdot\frac{1}{3}-\frac{1}{4}=5\frac{1}{6}\)

\(\Leftrightarrow\left(\frac{1}{4}-\frac{3x}{10}\right)\cdot\frac{1}{3}=\frac{31}{6}+\frac{1}{4}=\frac{65}{12}\)

\(\Leftrightarrow\frac{1}{4}-\frac{3x}{10}=\frac{65}{12}:\frac{1}{3}=\frac{65}{12}\cdot3=\frac{65}{4}\)

\(\Leftrightarrow\frac{3x}{10}=\frac{1}{4}-\frac{65}{4}=-16\)

\(\Leftrightarrow3x=-160\)

hay \(x=\frac{-160}{3}\)

Vậy: \(x=\frac{-160}{3}\)

d) Ta có: \(\frac{x-2}{-\frac{2}{9}}=\frac{-2}{x-2}\)

\(\Leftrightarrow\left(x-2\right)^2=-2\cdot\left(-\frac{2}{9}\right)=\frac{4}{9}\)

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

Vậy: \(x\in\left\{\frac{8}{3};\frac{4}{3}\right\}\)

a/ (x - 2)³ + \(\frac{8}{27}\) = 0

=> (x - 2)³ = 0 - \(\frac{8}{27}\) = \(\frac{-8}{27}\)

=> x - 2 = \(-\frac{2}{3}\)

=> x = \(-\frac{2}{3}+2=\frac{4}{3}\)

b/ \(4\frac{1}{3}:\frac{x}{4}=6:0,3\)

=> \(4\frac{1}{3}:\frac{x}{4}=6:\frac{3}{10}=6.\frac{10}{3}=20\)

=> \(\frac{x}{4}=4\frac{1}{3}:20=\frac{13}{3}.\frac{1}{20}=\frac{13}{60}\)

=> \(x=\frac{13}{60}.4=\frac{13}{15}\)

c/ \(\left(0,25-30\%x\right).\frac{1}{3}-\frac{1}{4}=5\frac{1}{6}\)

=> \(\left(0,25-30\%x\right).\frac{1}{3}=5\frac{1}{6}+\frac{1}{4}=\frac{65}{12}\)

=> \(0,25-\frac{30}{100}x=\frac{65}{12}:\frac{1}{3}=\frac{65}{12}.3=\frac{65}{4}\)

=> \(\frac{3}{10}x=0,25-\frac{65}{4}=\frac{1}{4}-\frac{65}{4}=-\frac{64}{4}=-16\)

=> \(x=-16:\frac{3}{10}=-16.\frac{10}{3}=-\frac{160}{3}\)

a) \(\frac{-3}{7}+x=\frac{1}{3}\)

\(\Leftrightarrow x=\frac{1}{3}+\frac{3}{7}\)

\(\Leftrightarrow x=\frac{16}{21}\)

b) \(\frac{-5}{8}+x=\frac{-2^2}{3}\)

\(\Leftrightarrow x=\frac{-4}{3}+\frac{5}{8}\)

\(\Leftrightarrow x=-\frac{17}{24}\)

c) \(4\frac{1}{3}:\frac{x}{4}=6:0,3\)

\(\Leftrightarrow\frac{8}{3}:\frac{x}{4}=20\)

\(\Leftrightarrow\frac{32}{3x}=20\)

\(\Leftrightarrow3x=\frac{8}{5}\)

\(\Leftrightarrow x=\frac{8}{15}\)

\(1\frac{2}{3}:\frac{x}{4}=6:0,3\)

\(\frac{5}{3}:\frac{x}{4}=20\)

\(\frac{x}{4}=\frac{5}{3}:20\)

\(\frac{x}{4}=\frac{1}{12}\)

\(\Rightarrow\frac{3x}{12}=\frac{1}{12}\)

\(\Rightarrow3x=1\)

\(\Rightarrow x=\frac{1}{3}\)

Vậy \(x=\frac{1}{3}\)

\(\frac{13}{3}:\frac{x}{4}=6:0,3\)

\(\frac{13}{3}:\frac{x}{4}=20\)

         \(\frac{x}{4}=\frac{13}{3}:20\)

         \(\frac{x}{4}=\frac{13}{3.20}\)

         \(\frac{x}{4}=\frac{13}{60}\)

\(60x=13.4\)

\(60x=52\)

     \(x=\frac{52}{60}\)

     \(x=\frac{13}{15}\)

Vậy \(x=\frac{13}{15}\)

\(\frac{1}{3}x:\frac{2}{3}=1\frac{3}{4}:\frac{2}{5}\)

\(\Rightarrow\frac{1}{3}x:\frac{2}{3}=\frac{35}{8}\)

\(\Rightarrow\frac{1}{3}x=\frac{35}{12}\)

\(\Rightarrow x=\frac{35}{4}\)

a) \(\left(\frac{1}{3}\cdot x\right):\frac{2}{3}=1\frac{3}{4}:\frac{2}{5}\)

\(=\left(\frac{1}{3}\cdot x\right):\frac{2}{3}=\frac{35}{8}\)

\(\Rightarrow\frac{1}{3}\cdot x=\frac{35}{8}\cdot\frac{2}{3}\)

\(\Rightarrow x=\frac{35}{12}:\frac{1}{3}=\frac{35}{4}\)

b) \(4,5:0,3=2,5:\left(0,1\cdot x\right)\)

\(=15=2,5:\left(0,1\cdot x\right)\)

\(\Rightarrow0,1\cdot x=2,25:15\)

\(\Rightarrow x=\frac{3}{20}:0,1=\frac{3}{2}=1,5\)

c) \(8:\left(\frac{1}{4}\cdot x\right)=2:0,02\)

\(8:\left(\frac{1}{4}\cdot x\right)=100\)

\(\Rightarrow\frac{1}{4}\cdot x=8:100\)

\(\Rightarrow x=\frac{2}{25}:\frac{1}{4}=\frac{8}{25}=0,32\)

d) \(3:2\frac{1}{4}=\frac{3}{4}:\left(6\cdot x\right)\)

\(=\frac{4}{3}=\frac{3}{4}:\left(6:x\right)\)

\(\Rightarrow6\cdot x=\frac{3}{4}:\frac{4}{3}\)

\(\Rightarrow x=\frac{9}{16}:6=\frac{3}{32}=0,09375\)

Tính:

b) \(\left(-2\right)^3.\left(\frac{3}{4}-0,25\right):\left(2\frac{1}{4}-1\frac{1}{6}\right)\)

\(=\left(-2\right)^3.\left(\frac{3}{4}-\frac{1}{4}\right):\left(\frac{9}{4}-\frac{7}{6}\right)\)

\(=\left(-8\right).\frac{1}{2}:\frac{13}{12}\)

\(=\left(-4\right):\frac{13}{12}\)

\(=-\frac{48}{13}.\)

Tìm x

a) \(4\frac{1}{3}:\frac{x}{4}=6:0,3\)

⇒ \(\frac{13}{3}:\frac{x}{4}=20\)

⇒ \(\frac{x}{4}=\frac{13}{3}:20\)

⇒ \(\frac{x}{4}=\frac{13}{60}\)

⇒ \(x.60=4.13\)

⇒ \(x.60=52\)

⇒ \(x=52:60\)

⇒ \(x=\frac{13}{15}\)

Vậy \(x=\frac{13}{15}.\)

b) \(\left(2^3:4\right).2^{x+1}=64\)

⇒ \(\left(8:4\right).2^{x+1}=64\)

⇒ \(2.2^{x+1}=64\)

⇒ \(2^{x+1}=64:2\)

⇒ \(2^{x+1}=32\)

⇒ \(2^{x+1}=2^5\)

⇒ \(x+1=5\)

⇒ \(x=5-1\)

⇒ \(x=4\)

Vậy \(x=4.\)

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