Tìm x, biết:
a) \(x.\dfrac{{21}}{{25}} = \dfrac{{ – 7}}{{10}}\)
b) \(\dfrac{{ – 3}}{{20}}x = \dfrac{5}{{12}} – \dfrac{2}{5}\)
c) \(\dfrac{2}{9}:x = \dfrac{1}{{18}}:0,375\)
d) \(\left( { – \dfrac{{11}}{{12}}} \right):2x = \dfrac{5}{2} + \dfrac{1}{4}\)
Tìm thừa số = tích : thừa số đã biết
Tìm số chia = số bị chia : thương
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\(\begin{array}{l}a)x.\dfrac{{21}}{{25}} = \dfrac{{ – 7}}{{10}}\\ \Leftrightarrow x = \dfrac{{ – 7}}{{10}}:\dfrac{{21}}{{25}}\\ \Leftrightarrow x = \dfrac{{ – 7}}{{10}}.\dfrac{{25}}{{21}}\\ \Leftrightarrow x = \dfrac{{ – 5}}{6}\end{array}\)
Vậy \(x = \dfrac{{ – 5}}{6}\)
\(\begin{array}{l}b)\dfrac{{ – 3}}{{20}}x = \dfrac{5}{{12}} – \dfrac{2}{5}\\ \Leftrightarrow \dfrac{{ – 3}}{{20}}x = \dfrac{{25}}{{60}} – \dfrac{{24}}{{60}}\\ \Leftrightarrow \dfrac{{ – 3}}{{20}}x = \dfrac{1}{{60}}\\ \Leftrightarrow x = \dfrac{1}{{60}}:\dfrac{{ – 3}}{{20}}\\ \Leftrightarrow x = \dfrac{1}{{60}}.\dfrac{{ – 20}}{3}\\ \Leftrightarrow x = \dfrac{{ – 1}}{9}\end{array}\)
Vậy \(x = \dfrac{{ – 1}}{9}\)
\(\begin{array}{l}c)\dfrac{2}{9}:x = \dfrac{1}{{18}}:0,375\\ \Leftrightarrow \dfrac{2}{9}:x = \dfrac{1}{{18}}:\dfrac{3}{8}\\ \Leftrightarrow \dfrac{2}{9}:x = \dfrac{1}{{18}}.\dfrac{8}{3}\\ \Leftrightarrow \dfrac{2}{9}:x = \dfrac{4}{{27}}\\ \Leftrightarrow x = \dfrac{2}{9}:\dfrac{4}{{27}}\\\Leftrightarrow x = \dfrac{2}{9}.\dfrac{27}{{4}}\\ \Leftrightarrow x = \dfrac{3}{2}\end{array}\)
Vậy \(x = \dfrac{3}{2}\)
\(\begin{array}{l}d)\left( { – \dfrac{{11}}{{12}}} \right):2x = \dfrac{5}{2} + \dfrac{1}{4}\\ \Leftrightarrow \left( { – \dfrac{{11}}{{12}}} \right):2x = \dfrac{{10}}{4} + \dfrac{1}{4}\\ \Leftrightarrow \left( { – \dfrac{{11}}{{12}}} \right):2x = \dfrac{{11}}{4}\\ \Leftrightarrow \left( { – \dfrac{{11}}{{12}}} \right):\dfrac{{11}}{4} = 2x\\ \Leftrightarrow \dfrac{{ – 11}}{{12}}.\dfrac{4}{{11}} = 2x\\ \Leftrightarrow \dfrac{{ – 1}}{3} = 2x\end{array}\)
\(\begin{array}{l} \Leftrightarrow x = \dfrac{{ – 1}}{3}:2\\\Leftrightarrow x = \dfrac{{ – 1}}{3}.\dfrac{1}{2}\\ \Leftrightarrow x = \dfrac{{ – 1}}{6}\end{array}\)
Vậy \(x = \dfrac{{ – 1}}{6}\)