|x+\(\dfrac{1}{3}\)| = \(\dfrac{11}{10}\)
Tính:
a) (6 : \(\dfrac{3}{5}\) \(1\dfrac{1}{6}\) x \(\dfrac{6}{7}\) ) : ( \(4\dfrac{1}{5}\) x \(\dfrac{10}{11}\) + \(5\dfrac{2}{11}\) )
b) (\(1-\dfrac{1}{2}\)) x (\(1-\dfrac{1}{3}\)) x (\(1-\dfrac{1}{4}\)) x ..... x (\(1-\dfrac{1}{2003}\)) x (\(1-\dfrac{1}{2007}\))
(x+\(\dfrac{2}{3}\))+\(\dfrac{1}{11}\)=(\(\dfrac{10}{-33}\).\(\dfrac{11}{8}\)).\(\dfrac{24}{-55}\)
\(\left(x+\dfrac{2}{3}\right)+\dfrac{1}{11}=\left(\dfrac{10}{-33}.\dfrac{11}{8}\right).\dfrac{24}{-55}\)
\(\Rightarrow\left(x+\dfrac{2}{3}\right)+\dfrac{1}{11}=\dfrac{-5}{12}.\dfrac{24}{-55}\)
\(\Rightarrow\left(x+\dfrac{2}{3}\right)+\dfrac{1}{11}=\dfrac{2}{11}\)
\(\Rightarrow x+\dfrac{2}{3}=\dfrac{2}{11}-\dfrac{1}{11}\)
\(\Rightarrow x+\dfrac{2}{3}=\dfrac{1}{11}\)
\(\Rightarrow x=\dfrac{1}{11}-\dfrac{2}{3}\)
\(\Rightarrow x=-\dfrac{19}{33}\)
(x + 2/3) + 1/11 = [10/(-33) . 11/8] . 24/(-55)
(x + 2/3) + 1/11 = -5/12 . 24/(-55)
(x + 2/3) + 1/11 = 2/11
x + 2/3 = 2/11 - 1/11
x + 2/3 = 1/11
x = 1/11 - 2/3
x = -19/33
Bài 1:Tính hợp lí
a)-12,5+17,55-3,5+2,45
b)0,175-(\(2\dfrac{1}{3}\)+0,175)
c)\(\dfrac{5}{13}\).\(\dfrac{-3}{10}\)+\(\dfrac{3}{10}\).\(\dfrac{-8}{13}\)+(-0,7)
Bài 2:Tìm x biết
a)x+\(\dfrac{2}{5}\)=2,4
b)2x-\(\dfrac{4}{5}\)=-1,5
c)11-(15+11)=x-(25-9)
Bài 3:Cho A=\(\dfrac{1}{2^2}\)+\(\dfrac{1}{3^2}\)+\(\dfrac{1}{4^2}\)+\(\dfrac{1}{5^2}\)+....+\(\dfrac{1}{100^2}\)
Chứng tỏ A<1
2:
a: x=2,4-0,4=2
b: =>2x=-1,5+0,8=-0,7
=>x=-0,35
c: =>x-16=-15
=>x=1
Tìm x biết
a) \(\dfrac{x}{3}=\dfrac{7}{25}+\dfrac{-1}{5}\)
b)\(\dfrac{4}{9}+\dfrac{x}{5}=\dfrac{5}{11}\)
c) \(\dfrac{-5}{9}+\dfrac{x}{10}=\dfrac{1}{3}\)
a) Ta có: \(\dfrac{x}{3}=\dfrac{7}{25}+\dfrac{-1}{5}\)
\(\Leftrightarrow\dfrac{x}{3}=\dfrac{7}{25}+\dfrac{-5}{25}=\dfrac{2}{25}\)
hay \(x=\dfrac{6}{25}\)
Vậy: \(x=\dfrac{6}{25}\)
b) Ta có: \(\dfrac{4}{9}+\dfrac{x}{5}=\dfrac{5}{11}\)
\(\Leftrightarrow\dfrac{x}{5}=\dfrac{5}{11}-\dfrac{4}{9}=\dfrac{45}{99}-\dfrac{44}{99}=\dfrac{1}{99}\)
hay \(x=\dfrac{5}{99}\)
Vậy: \(x=\dfrac{5}{99}\)
c) Ta có: \(\dfrac{-5}{9}+\dfrac{x}{10}=\dfrac{1}{3}\)
\(\Leftrightarrow\dfrac{x}{10}=\dfrac{1}{3}+\dfrac{5}{9}=\dfrac{3}{9}+\dfrac{5}{9}=\dfrac{8}{9}\)
hay \(x=\dfrac{80}{9}\)
Vậy: \(x=\dfrac{80}{9}\)
\(\dfrac{x+4}{8}+\dfrac{x+3}{9}=\dfrac{x+2}{10}+\dfrac{x+1}{11}\)
\(\dfrac{x+4}{8}+\dfrac{x+3}{9}=\dfrac{x+2}{10}+\dfrac{x+1}{11}\)
\(\Leftrightarrow\left(\dfrac{x+4}{8}+1\right)+\left(\dfrac{x+3}{9}+1\right)=\left(\dfrac{x+2}{10}+1\right)+\left(\dfrac{x+1}{11}+1\right)\)
\(\Leftrightarrow\dfrac{x+12}{8}+\dfrac{x+12}{9}-\dfrac{x+12}{10}-\dfrac{x+12}{11}=0\)
\(\Leftrightarrow\left(x+12\right)\left(\dfrac{1}{8}+\dfrac{1}{9}-\dfrac{1}{10}-\dfrac{1}{11}\right)=0\)
\(\Leftrightarrow x=-12\)( do \(\dfrac{1}{8}+\dfrac{1}{9}-\dfrac{1}{10}-\dfrac{1}{11}\ne0\))
\(\dfrac{x+4}{8}+\dfrac{x+3}{9}=\dfrac{x+2}{10}+\dfrac{x+1}{11}\)
\(\dfrac{x+4}{8}+1+\dfrac{x+3}{9}+1=\dfrac{x+2}{10}+1+\dfrac{x+1}{11}+1\)
\(\dfrac{x+12}{8}+\dfrac{x+12}{9}=\dfrac{x+12}{10}+\dfrac{x+12}{11}\)
\(\dfrac{x+12}{8}+\dfrac{x+12}{9}-\dfrac{x+12}{10}-\dfrac{x+12}{11}=0\)
\(\Rightarrow\left(x+12\right).\left(\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10}+\dfrac{1}{11}\right)=0\)
Vì \(\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10}+\dfrac{1}{11}\ne0\) nên \(x+12=0\)
\(\Rightarrow x=-12\)
\(\Rightarrow\left(\dfrac{x+4}{8}+1\right)+\left(\dfrac{x+3}{9}+1\right)=\left(\dfrac{x+2}{10}+1\right)+\left(\dfrac{x+1}{11}+1\right)\\ \Rightarrow\dfrac{x+12}{8}+\dfrac{x+12}{9}=\dfrac{x+12}{10}+\dfrac{x+12}{11}\\ \Rightarrow\left(x+12\right)\left(\dfrac{1}{8}+\dfrac{1}{9}-\dfrac{1}{10}-\dfrac{1}{11}\right)=0\\ \Rightarrow x+12=0\left(\dfrac{1}{8}+\dfrac{1}{9}-\dfrac{1}{10}-\dfrac{1}{11}\ne0\right)\\ \Rightarrow x=-12\)
tìm x
\([\dfrac{6:\dfrac{3}{5}-1\dfrac{1}{16}.\dfrac{16}{7}}{4\dfrac{1}{5}-\dfrac{10}{11}+5\dfrac{2}{11}}-\dfrac{\left(\dfrac{3}{20}+\dfrac{1}{2}-\dfrac{1}{5}\right).\dfrac{12}{49}}{3\dfrac{1}{3}+\dfrac{2}{9}}].x=2\dfrac{23}{96}\)
a.,\(\dfrac{4}{5}+5\dfrac{1}{2}\text{x }\left(4,5-2\right)=\dfrac{7}{10}\) b,125%x\(\dfrac{17}{4}:\left(1\dfrac{5}{16}-0,5\right)+2008\)
c,\(\dfrac{5}{11}+\left(\dfrac{16}{11}+1\right)\) d, \(\dfrac{3}{17}+\dfrac{11}{4}+\dfrac{5}{8}+\dfrac{14}{17}+\dfrac{3}{8}\)
`a)4/5+5 1/2 xx (4,5-2)+7/10`
`=4/5+11/2*2,5+7/10`
`=0,8+2,2+0,7`
`=3+0,7=3,7`
`b)125%xx 17/4:(1 5/16-0,5)+2008`
`=1,25xx4,25:13/16+2008`
`=85/13+2008`
`=2014 7/13`
`c)5/11+(16/11+1)`
`=5/11+1+5/11+1`
`=2+10/11=32/11`
`d)3/17+11/4+5/8+14/17+3/8`
`=3/17+14/17+5/8+3/8+11/4`
`=1+1+11/4`
`=19/4`
a)
\(\dfrac{4}{5}+5\dfrac{1}{2}x\left(4,5-2\right)=\dfrac{7}{10}\)
<=> \(\dfrac{11}{2}x\times2,5=\dfrac{7}{10}-\dfrac{4}{5}=\dfrac{-1}{10}\)
<=> \(\dfrac{55}{4}x=\dfrac{-1}{10}< =>x=\dfrac{-2}{275}\)
b) \(125\%\times\dfrac{17}{4}:\left(1\dfrac{5}{16}-0,5\right)+2008\)
= \(\dfrac{85}{16}:\left(\dfrac{21}{16}-\dfrac{1}{2}\right)+2008=\dfrac{85}{16}:\dfrac{13}{16}+2008=\dfrac{26189}{13}\)
c) \(\dfrac{5}{11}+\left(\dfrac{16}{11}+1\right)\)
= \(\dfrac{21}{11}+1=\dfrac{32}{11}\)
d) \(\left(\dfrac{3}{17}+\dfrac{14}{17}\right)+\left(\dfrac{5}{8}+\dfrac{3}{8}\right)+\dfrac{11}{4}\)
= 1 + 1 + \(\dfrac{11}{4}\) = \(\dfrac{19}{4}\)
giải phương trình sau:
a) \(\dfrac{8}{x-8}+\dfrac{11}{x-11}=\dfrac{9}{x-9}+\dfrac{10}{x-10}\)
b) \(\dfrac{x}{x-3}-\dfrac{x}{x-5}=\dfrac{x}{x-4}-\dfrac{x}{x-6}\)
c) \(\dfrac{4}{x^2-3x+2}-\dfrac{3}{2x^2-6x+1}+1=0\)
d) \(\dfrac{1}{x-1}+\dfrac{2}{x-2}+\dfrac{3}{x-3}=\dfrac{6}{x-6}\)
a/\(\dfrac{8}{x-8}+1+\dfrac{11}{x-11}+1=\dfrac{9}{x-9}+1+\dfrac{10}{x-10}+1\)
=>\(\dfrac{8+x-8}{x-8}+\dfrac{11+x-11}{x-11}=\dfrac{9+x-9}{x-9}+\dfrac{10+x-10}{x-10}\)
=>\(\dfrac{x}{x-8}+\dfrac{x}{x-11}-\dfrac{x}{x-9}-\dfrac{x}{x-10}=0\)
=>x.\(\left(\dfrac{1}{x-8}+\dfrac{1}{x-11}+\dfrac{1}{x-9}+\dfrac{1}{x-10}\right)=0\)
=>x=0
b/\(\dfrac{x}{x-3}-1+\dfrac{x}{x-5}-1=\dfrac{x}{x-4}-1+\dfrac{x}{x-6}-1\)
=>\(\dfrac{x-x+3}{x-3}+\dfrac{x-x+5}{x-5}-\dfrac{x-x+4}{x-4}-\dfrac{x-6+6}{x-6}=0\)
=>\(\dfrac{3}{x-3}+\dfrac{5}{x-5}-\dfrac{4}{x-4}-\dfrac{6}{x-6}=0\)
Đến đây thì bạn giải giống câu a
Giải các phương trình sau:
\(e.\dfrac{12}{1-9x^2}=\dfrac{1-3x}{1+3x}-\dfrac{1+3x}{1-3x}\)
\(f.\dfrac{6x+1}{x^2-7x+10}+\dfrac{5}{x-2}=\dfrac{3}{x-5}\)
\(g.\dfrac{2}{x+2}-\dfrac{2x^2+16}{x^3+8}=\dfrac{5}{x^2-2x+4}\)
\(h.\dfrac{8}{x-8}+\dfrac{11}{x-11}=\dfrac{9}{x-9}+\dfrac{10}{x-10}\)
e) ĐK : \(\left\{{}\begin{matrix}1+3x\ne0\\1-3x\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x\ne-1\\3x\ne1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne\dfrac{-1}{3}\\x\ne\dfrac{1}{3}\end{matrix}\right.\)
\(\Leftrightarrow\dfrac{12}{\left(1-3x\right)\left(1+3x\right)}=\dfrac{\left(1-3x\right)^2-\left(1+3x\right)^2}{\left(1+3x\right)\left(1-3x\right)}\)
\(\Leftrightarrow12\left(1+3x\right)\left(1-3x\right)=\left(1-3x\right)\left(1+3x\right)\left(1-3x-1-3x\right)\left(1-3x+1+3x\right)\)
\(\Leftrightarrow12=\left(-6x\right).2\Leftrightarrow6=-6x\)
\(\Leftrightarrow x=-1\left(TM\right)\)
\(\dfrac{11}{10}.x-\dfrac{1}{3}=\dfrac{2}{5}\)
=>11/10x=2/5+1/3=6/15+5/15=11/15
nên x=2/3
\(\dfrac{11}{10}.x-\dfrac{1}{3}=\dfrac{2}{5}\)
\(\dfrac{11}{10}.x=\dfrac{2}{5}+\dfrac{1}{3}\)
\(\dfrac{11}{10}.x=\dfrac{11}{15}\)
\(x=\dfrac{11}{15}:\dfrac{11}{10}\)
\(x=\dfrac{2}{3}\)
vậy x=...
11/10.X-1/3=2/5
11/10.X=2/5+1/3
11/10.X=11/15
X=11/15:11/10
X=2/3