Toán Lớp 6: tìm x biết x/10 + x+1/9 + x+2/8 + x+3/7=x+4/6 + x+5/5 + x+6/4 + x+7/3
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Toán Lớp 6: tìm x biết x/10 + x+1/9 + x+2/8 + x+3/7=x+4/6 + x+5/5 + x+6/4 + x+7/3
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$\dfrac{x}{10}+\dfrac{1}{9}+\dfrac{1}{4}+\dfrac{3}{7}=\dfrac{4}{6}+\dfrac{5}{5}+\dfrac{6}{4}+x+\dfrac{7}{3}$
$⇒\dfrac{199}{252}+\dfrac{x}{10}=\dfrac{4}{6}+\dfrac{5}{5}+\dfrac{6}{4}+x+\dfrac{7}{3}$
$⇒\dfrac{199}{252}+\dfrac{x}{10}-\dfrac{199}{252}=x+\dfrac{11}{2}-\dfrac{199}{252}$
$⇒\dfrac{x}{10}=x+\dfrac{1187}{252}$
$⇒\dfrac{x}{10}\cdot \:10=x\cdot \:10+\dfrac{1187}{252}\cdot \:10$
$⇒x=x\cdot \:10+\dfrac{5935}{126}$
$⇒x-x\cdot \:10=x\cdot \:10+\dfrac{5935}{126}-x\cdot \:10$
$⇒-9x=\dfrac{5935}{126}$
$⇒\dfrac{-9x}{-9}=\dfrac{\dfrac{5935}{126}}{-9}$
$⇒x=-\dfrac{5935}{1134}$
Vậy $x=-\dfrac{5935}{1134}$