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a) \(2,5:\left(4x\right)=0,5:0,2\)
\(\Leftrightarrow\frac{5}{2}.\frac{1}{4x}=\frac{1}{2}.5\)
\(\Leftrightarrow\frac{5}{2}.\frac{1}{4x}=\frac{5}{2}\)
\(\Leftrightarrow\frac{1}{4x}=\frac{5}{2}:\frac{5}{2}\)
\(\Leftrightarrow\frac{1}{4x}=1\)
\(\Leftrightarrow4x=1\)
\(\Leftrightarrow x=\frac{1}{4}\)
Vậy : \(x=\frac{1}{4}\)
b) \(\frac{1}{5}x:3=\frac{2}{3}:0,25\)
\(\Leftrightarrow\frac{x}{5}.\frac{1}{3}=\frac{2}{3}:\frac{1}{4}\)
\(\Leftrightarrow\frac{x}{15}=\frac{2}{3}.4=\frac{8}{3}\)
\(\Leftrightarrow x=\frac{8}{3}.15\)
\(\Leftrightarrow x=40\)
Vậy : \(x=40\)
c) \(1,25:0,8=\frac{3}{8}:\left(0,2x\right)\)
\(\Leftrightarrow\frac{5}{4}:\frac{4}{5}=\frac{3}{8}:\frac{x}{5}\)
\(\Leftrightarrow\frac{25}{16}=\frac{3}{8}.\frac{5}{x}\)
\(\Leftrightarrow\frac{25}{16}=\frac{15}{8x}\)
\(\Leftrightarrow25.8x=15.16\)
\(\Leftrightarrow8x=\frac{15.16}{25}=\frac{48}{5}\)
\(\Leftrightarrow x=\frac{48}{5}:8\)
\(\Leftrightarrow x=\frac{6}{5}\)
Vậy : \(x=\frac{6}{5}\)
d) \(13\frac{1}{3}:1\frac{1}{3}=26:\left(2x-1\right)\)
\(\Leftrightarrow\frac{40}{3}.\frac{3}{4}=26:\left(2x-1\right)\)
\(\Leftrightarrow10=26:\left(2x-1\right)\)
\(\Leftrightarrow2x-1=\frac{26}{10}=\frac{13}{5}\)
\(\Leftrightarrow2x=\frac{13}{5}+1=\frac{18}{5}\)
\(\Leftrightarrow x=\frac{18}{5}:2\)
\(\Leftrightarrow x=\frac{9}{5}\)
Vậy : \(x=\frac{9}{5}\)
e) \(0,2:1\frac{1}{5}=\frac{2}{3}:\left(6x+7\right)\)
\(\Leftrightarrow\frac{1}{5}.\frac{5}{6}=\frac{2}{3}:\left(6x+7\right)\)
\(\Leftrightarrow\frac{1}{6}=\frac{2}{3}:\left(6x+7\right)\)
\(\Leftrightarrow6x+7=\frac{2}{3}:\frac{1}{6}=4\)
\(\Leftrightarrow6x=4-7=-3\)
\(\Leftrightarrow x=-\frac{3}{6}=-\frac{1}{2}\)
Vậy : \(x=-\frac{1}{2}\)
f) \(\frac{37-x}{x+13}=\frac{3}{7}\)
\(\Leftrightarrow\left(37-x\right).7=3.\left(x+13\right)\)
\(\Leftrightarrow37.7-7x=3x+3.13\)
\(\Leftrightarrow259-7x=3x+39\)
\(\Leftrightarrow-7x-3x=39-259\)
\(\Leftrightarrow-10x=-220\)
\(\Leftrightarrow x=\frac{-220}{-10}=22\)
Vậy : \(x=22\)
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