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c ) 5 / x - 4 / 3 = 1 / 6
5 / x = 4 / 3
5 . 3 = x . 4
15 = x . 4
x = 15 . 4
x = 60
5 / x = 1 / 6
5 . 6 = x . 1
30 = x . 1
x = 30 . 1
x = 30
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Trả lời:
\(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{\left(5x+1\right)\left(5x+6\right)}=\frac{2005}{2006}\)
\(\Rightarrow1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{5x+1}-\frac{1}{5x+6}=\frac{2005}{2006}\)
\(\Rightarrow1-\frac{1}{5x+6}=\frac{2005}{2006}\)
\(\Rightarrow\frac{1}{5x+6}=1-\frac{2005}{2006}\)
\(\Rightarrow\frac{1}{5x+6}=\frac{1}{2006}\)
\(\Rightarrow5x+6=2006\)
\(\Rightarrow5x=2000\)
\(\Rightarrow x=400\)
Vậy x = 400
Trả lời:
\(\frac{x}{2008}-\frac{1}{10}-\frac{1}{15}-\frac{1}{21}-...-\frac{1}{120}=\frac{5}{8}\)
\(\Rightarrow\frac{x}{2008}-\left(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\right)=\frac{5}{8}\)\(\frac{5}{8}\)
Đặt \(A=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\), ta được : \(\frac{x}{2008}-A=\frac{5}{8}\) (*)
\(\Rightarrow A=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)
\(\Rightarrow A=2\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\right)\)
\(\Rightarrow A=2\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\right)\)
\(\Rightarrow A=2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(\Rightarrow A=2\left(\frac{1}{4}-\frac{1}{16}\right)=2.\frac{3}{16}=\frac{3}{8}\)
Thay A vào (*) , ta có:
\(\frac{x}{2008}-\frac{3}{8}=\frac{5}{8}\)
\(\Rightarrow\frac{x}{2008}=1\)
\(\Rightarrow x=2008\)
Vậy x = 2008
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a, 230 + [32 + (x - 5)] =315
32 + (x-5) = 315 - 230
32 + (x-5) =85
x-5=85-32
x-5=53
x=53+5
x=58
\(a,3x+17=-5\\ \Rightarrow3x=-22\\ \Rightarrow x=-\dfrac{22}{3}\\ b,\dfrac{-5}{8}=\dfrac{x}{16}\\ \Rightarrow x=\dfrac{-5}{8}.16\\ \Rightarrow x=-10\\ c,\dfrac{4}{9}+\dfrac{7}{3}:x=\dfrac{1}{5}\\ \Rightarrow\dfrac{7}{3}:x=-\dfrac{11}{45}\\ \Rightarrow x=-\dfrac{105}{11}\)
\(a)3.x+17=-5\)
\(3.x\) \(=\left(-5\right)-170=-22\)
\(x\) \(=\left(-22\right)\div3\)
\(x\) \(=\dfrac{-22}{3}\)
\(b)\dfrac{-5}{8}=\dfrac{x}{16}\)
\(\Rightarrow x=\dfrac{\left(-5\right)\times16}{8}=\dfrac{-80}{8}=-10\)
\(c)\dfrac{4}{9}+\dfrac{7}{3}:x=\dfrac{1}{5}\)
\(\dfrac{7}{3}:x=\dfrac{1}{5}-\dfrac{4}{9}\)
\(\dfrac{7}{3}:x=\dfrac{1}{5}+\left(\dfrac{-4}{9}\right)=\dfrac{9}{45}+\left(\dfrac{-20}{45}\right)=\dfrac{-11}{45}\)
\(x=\dfrac{7}{3}:\left(\dfrac{-11}{45}\right)=\dfrac{7}{3}\times\left(\dfrac{-45}{11}\right)\)
\(x=\dfrac{-315}{33}=\dfrac{-105}{11}\)