Bài 1 :Tìm x, biết :
a, \(2\dfrac{1}{3}:\dfrac{1}{3}\) = \(\dfrac{7}{9}:x\)
b, \(x:\dfrac{1}{3}=\dfrac{12}{99}:\dfrac{15}{90}\)
c, \(\dfrac{4}{9}:x=3\dfrac{1}{3}:2,25\)
d, \(\dfrac{4}{3}:\dfrac{41}{99}=x:\dfrac{75}{90}\)
e, \(\dfrac{x-5}{7}=\dfrac{x+2}{3}\)
f, \(\left(x-5\right).\left(x+2\right)=\left(x-3\right).\left(x+4\right)\)
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e) \(\dfrac{x-5}{7}=\dfrac{x+2}{3}\Leftrightarrow3\left(x-5\right)=7\left(x+2\right)\Leftrightarrow3x-15=7x+14\)
\(\Leftrightarrow7x-3x=-15-14\Leftrightarrow4x=-29\Leftrightarrow x=\dfrac{-29}{4}\) vậy \(x=\dfrac{-29}{4}\)
f) \(\left(x-5\right)\left(x+2\right)=\left(x-3\right)\left(x+4\right)\Leftrightarrow x^2+2x-5x-10=x^2+4x-3x-12\)
\(\Leftrightarrow x^2+2x-5x-10-x^2-4x+3x+12=0\Leftrightarrow-4x+2=0\Leftrightarrow4x=2\Leftrightarrow x=\dfrac{2}{4}=\dfrac{1}{2}\)
vậy \(x=\dfrac{1}{2}\)
a, \(2\dfrac{1}{3}:\dfrac{1}{3}=\dfrac{7}{9}:x\)
\(\Rightarrow\dfrac{7}{9}:x=\dfrac{7}{3}\cdot3\)
\(\Rightarrow\dfrac{7}{9}:x=7\)
\(\Rightarrow x=\dfrac{1}{9}\)
b, \(x:\dfrac{1}{3}=\dfrac{12}{99}:\dfrac{15}{90}\)
\(\Rightarrow x:\dfrac{1}{3}=\dfrac{4}{33}\cdot\dfrac{3}{18}\)
\(\Rightarrow x:\dfrac{1}{3}=\dfrac{2}{99}\)
\(\Rightarrow x=\dfrac{2}{297}\)
c, \(\dfrac{4}{9}:x=3\dfrac{1}{3}:2,25\)
\(\Rightarrow\dfrac{4}{9}:x=\dfrac{10}{3}\cdot\dfrac{4}{9}\)
\(\Rightarrow\dfrac{4}{9}:x=\dfrac{40}{27}\)
\(\Rightarrow x=\dfrac{3}{10}\)
d, \(\dfrac{4}{3}:\dfrac{41}{99}=x:\dfrac{75}{90}\)
\(\Rightarrow x:\dfrac{5}{6}=\dfrac{4}{3}\cdot\dfrac{99}{41}\)
\(\Rightarrow x:\dfrac{5}{6}=\dfrac{132}{41}\)
\(\Rightarrow x=\dfrac{110}{41}\)
e, \(\dfrac{x-5}{7}=\dfrac{x+2}{3}\)
\(\Rightarrow3\left(x-5\right)=7\left(x+2\right)\)
\(\Rightarrow3x-15=7x+14\)
\(\Rightarrow7x-3x=-15-14\)
\(\Rightarrow4x=-29\)
\(\Rightarrow x=-\dfrac{29}{4}\)
f, \(\left(x-5\right)\cdot\left(x+2\right)=\left(x-3\right)\cdot\left(x+4\right)\)
\(\Rightarrow x^2+2x-5x-10=x^2+4x-3x-12\)
\(\Rightarrow x^2-3x-10=x^2+x-12\)
\(\Rightarrow x^2-x^2-3x-x=-12+10\)
\(\Rightarrow-4x=2\)
\(\Rightarrow x=-0,5\)
