Nhân chéo:
2(x - 2) = 3(x - 1)
=> 2x - 4 = 3x - 3
=> 2x - 3x = 4 - 3
=> -1x = 1
=> x = -1
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1. So sánh:a. 1 và frac{1}{2}+frac{1}{2^2}+frac{1}{2^3}+.....+frac{1}{2^{50}}b. frac{1}{3}+frac{1}{3^2}+frac{1}{3^3}+.....+frac{1}{3^{100}}với frac{1}{2}c. frac{1}{4}+frac{1}{4^2}+frac{1}{4^6}+.....frac{1}{4^{1000}}với frac{1}{3}2. Tìm x, biết:a.left(frac{2}{5}-xright):1frac{1}{3}+frac{1}{2}-4b.3-frac{1-frac{1}{2}}{1+frac{1}{x}}2frac{2}{3}c.4^x+4^{x+3}4160d.2^{x-1}+5.2^{x-2}frac{7}{32}e.frac{x-100}{24}+frac{x-98}{26}+frac{x-96}{24}3g.frac{x-1}{65}+frac{x-3}{63}+frac{x-5}{61}+frac{x-7}{59}
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1. So sánh:
a. 1 và \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+.....+\frac{1}{2^{50}}\)
b. \(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+.....+\frac{1}{3^{100}}\)với \(\frac{1}{2}\)
c. \(\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^6}+.....\frac{1}{4^{1000}}\)với \(\frac{1}{3}\)
2. Tìm x, biết:
a.\(\left(\frac{2}{5}-x\right):1\frac{1}{3}+\frac{1}{2}=-4\)
b.\(3-\frac{1-\frac{1}{2}}{1+\frac{1}{x}}=2\frac{2}{3}\)
c.\(4^x+4^{x+3}=4160\)
d.\(2^{x-1}+5.2^{x-2}=\frac{7}{32}\)
e.\(\frac{x-100}{24}+\frac{x-98}{26}+\frac{x-96}{24}=3\)
g.\(\frac{x-1}{65}+\frac{x-3}{63}+=\frac{x-5}{61}+\frac{x-7}{59}\)
Tìm x,y biết : |x-y|1frac{1}{2}a)frac{-1}{2}+left(x-3right):frac{-1}{2}-1frac{2}{3}c)left(frac{1}{3}-xright)^2frac{1}{4} b)2,25+frac{3}{2}:left(x-5right)2frac{1}{2}d)frac{3}{2}+frac{x-1}{3}1e)frac{-6}{8}+frac{x}{12}frac{5}{6}g)frac{1}{2}-frac{1}{3}left(x-2right)frac{-2}{3}h)frac{5}{2}left(x+1right)-frac{1}{2}3frac{1}{2}k)frac{x}{3}-frac{1}{2}-2left(x+1right)+3
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Tìm x,y biết : |x-y|=1\(\frac{1}{2}\)
a)\(\frac{-1}{2}+\left(x-3\right):\frac{-1}{2}=-1\frac{2}{3}\)
c)\(\left(\frac{1}{3}-x\right)^2=\frac{1}{4}\)
b)\(2,25+\frac{3}{2}:\left(x-5\right)=2\frac{1}{2}\)
d)\(\frac{3}{2}+\frac{x-1}{3}=1\)
e)\(\frac{-6}{8}+\frac{x}{12}=\frac{5}{6}\)
g)\(\frac{1}{2}-\frac{1}{3}\left(x-2\right)=\frac{-2}{3}\)
h)\(\frac{5}{2}\left(x+1\right)-\frac{1}{2}=3\frac{1}{2}\)
k)\(\frac{x}{3}-\frac{1}{2}=-2\left(x+1\right)+3\)
tim xa)2frac{3}{4}x-1frac{5}{8}x1b)2frac{3}{4}x-1frac{5}{8}x1c)frac{3}{2}x-frac{2}{5}frac{1}{3}x-frac{1}{4}d)2x-frac{1}{4}frac{5}{6}-frac{1}{2}xe)frac{-5}{6}+3xfrac{2}{3}-frac{1}{2}xf)frac{5}{2}x-frac{3}{2}x+frac{29}{10}g)frac{2}{3}+frac{7}{3}xfrac{5}{4}x+frac{1}{6}h)frac{1}{3}.x+frac{2}{5}left(x-1right)0giup mk nha moi nguoi
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tim x
a)\(2\frac{3}{4}x-1\frac{5}{8}x=1\)
b)\(2\frac{3}{4}x-1\frac{5}{8}x=1\)
c)\(\frac{3}{2}x-\frac{2}{5}=\frac{1}{3}x-\frac{1}{4}\)
d)\(2x-\frac{1}{4}=\frac{5}{6}-\frac{1}{2}x\)
e)\(\frac{-5}{6}+3x=\frac{2}{3}-\frac{1}{2}x\)
f)\(\frac{5}{2}x-\frac{3}{2}=x+\frac{29}{10}\)
g)\(\frac{2}{3}+\frac{7}{3}x=\frac{5}{4}x+\frac{1}{6}\)
h)\(\frac{1}{3}.x+\frac{2}{5}\left(x-1\right)=0\)
giup mk nha moi nguoi
\(\frac{1}{2}x+2\frac{1}{2}=3\frac{1}{2}x-\frac{3}{4}\)
\(\frac{1}{3}x+\frac{2}{5}\left\{x+1\right\}=0\)
\(\frac{2}{3}-\frac{1}{3}\left\{x-\frac{3}{2}\right\}-\frac{1}{2}\left\{2x+1\right\}=5\)
Tìm x:
a) \(\frac{1}{2}x+2\frac{1}{2}=3\frac{1}{2}x-\frac{3}{4}\)
b) \(\frac{2}{3}x-\frac{2}{5}=\frac{1}{2}x-\frac{1}{3}\)
c) \(\frac{1}{3}x+\frac{2}{5}\left(x+1\right)=0\)
tìm x
\(\frac{4}{5}x^2\left(\frac{x}{3}-\frac{1}{2}\right)-\left(\frac{1}{2}x-\frac{2}{3}\right)\left(\frac{4x^2}{3}+1\right)=\frac{22}{45}x^2\)
Tìm x, biết:a)-3frac{1}{2}+frac{1}{3}.left(x-1right)-1frac{1}{3}:2frac{1}{3}b)frac{x-1}{4}frac{x-2}{5}c)frac{x}{0,04}frac{0,09}{x}d)4:left(x-1right)left(x-1right):9e)3frac{1}{2}:x.frac{1}{2}5frac{1}{3}:frac{1}{2}.frac{1}{5}f)/2x-3/5g)left(2x-frac{1}{3}right)^2left(13xright)^2h) left(3-frac{1}{2}:xright)^2frac{1}{4}i) left(3-1frac{1}{2}:xright)^3frac{1}{8}
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Tìm x, biết:
a)\(-3\frac{1}{2}+\frac{1}{3}.\left(x-1\right)=-1\frac{1}{3}:2\frac{1}{3}\)
b)\(\frac{x-1}{4}=\frac{x-2}{5}\)
c)\(\frac{x}{0,04}=\frac{0,09}{x}\)
d)\(4:\left(x-1\right)=\left(x-1\right):9\)
e)\(3\frac{1}{2}:x.\frac{1}{2}=5\frac{1}{3}:\frac{1}{2}.\frac{1}{5}\)
f)/2x-3/=5
g)\(\left(2x-\frac{1}{3}\right)^2=\left(1=3x\right)^2\)
h) \(\left(3-\frac{1}{2}:x\right)^2=\frac{1}{4}\)
i) \(\left(3-1\frac{1}{2}:x\right)^3=\frac{1}{8}\)
Tìm x biết frac{x+2}{327}+frac{x+3}{326}+frac{x+4}{325}+frac{x+5}{324}+frac{x+349}{5}0CMR:frac{1}{2!}+frac{2}{3!}+frac{3}{4!}+...+frac{99}{100!} 1frac{1}{sqrt{1}}+frac{1}{sqrt{2}}+frac{1}{sqrt{3}}+...+frac{1}{sqrt{100}}10Tính B1+frac{1}{2}left(1+2right)+frac{1}{3}left(1+2+3right)+frac{1}{4}left(1+2+3+4right)+...+frac{1}{20}left(1+2+3+...+20right)
Đọc tiếp
Tìm x biết \(\frac{x+2}{327}+\frac{x+3}{326}+\frac{x+4}{325}+\frac{x+5}{324}+\frac{x+349}{5}=0\)
CMR:\(\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+...+\frac{99}{100!}< 1\)
\(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{100}}>10\)
Tính \(B=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+\frac{1}{4}\left(1+2+3+4\right)+...+\frac{1}{20}\left(1+2+3+...+20\right)\)
Bài 1 : Thực hiện phép tính(1) D 1+frac{1}{2}left(1+2right)+frac{1}{3}left(1+2+3right)+...+frac{1}{16}left(1+2+...+16right)(2) M frac{frac{1}{99}+frac{2}{98}+frac{3}{97}+...+frac{99}{1}}{frac{1}{2}+frac{1}{3}+frac{1}{4}+...+frac{1}{100}}Bài 2 : Tìm x biết(1) x-left{x-left[x-left(-x+1right)right]right}1(2) left[frac{1}{2}+frac{1}{3}+...+frac{1}{2016}right]cdot xfrac{2015}{1}+frac{2014}{2}+...+frac{1}{2015}(3) frac{x}{left(a+5right)left(4-aright)}frac{1}{a+5}+frac{1}{4-a}(4) frac{x+2}{11}+frac{x+...
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Bài 1 : Thực hiện phép tính
(1) D = \(1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{16}\left(1+2+...+16\right)\)
(2) M =\(\frac{\frac{1}{99}+\frac{2}{98}+\frac{3}{97}+...+\frac{99}{1}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)
Bài 2 : Tìm x biết
(1) \(x-\left\{x-\left[x-\left(-x+1\right)\right]\right\}=1\)
(2) \(\left[\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2016}\right]\cdot x=\frac{2015}{1}+\frac{2014}{2}+...+\frac{1}{2015}\)
(3) \(\frac{x}{\left(a+5\right)\left(4-a\right)}=\frac{1}{a+5}+\frac{1}{4-a}\)
(4) \(\frac{x+2}{11}+\frac{x+2}{12}+\frac{x+2}{13}=\frac{x+2}{14}+\frac{x+2}{15}\)
(5) \(\frac{x+1}{2015}+\frac{x+2}{2014}+\frac{x+3}{2013}+\frac{x+4}{2012}+4=0\)
Bài 3 :
(1) Cho : A =\(\frac{9}{1}+\frac{8}{2}+\frac{7}{3}+...+\frac{1}{9}\); B =\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}\)
CMR : \(\frac{A}{B}\)Là 1 số nguyên
(2) Cho : D =\(\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+...+\frac{1}{2000}\)CMR : \(D< \frac{3}{4}\)
Bài 4 : Ký hiệu [x] là số nguyên lớn nhất không vượt quá x , gọi là phần nguyên của x.
VD : [1.5] =1 ; [3] =3 ; [-3.5] = -4
(1) Tính :\(\left[\frac{100}{3}\right]+\left[\frac{100}{3^2}\right]+\left[\frac{100}{3^3}\right]+\left[\frac{100}{3^4}\right]\)
(2) So sánh : A =\(\left[X\right]+\left[X+\frac{1}{5}\right]+\left[X+\frac{2}{5}\right]+\left[X+\frac{3}{5}\right]+\left[X+\frac{4}{5}\right]\)và B = [5x]. Biết x=3.7
Tìm x biết:
1) \(\frac{x+1}{2}+\frac{x+1}{3}+\frac{x+1}{4}=\frac{x+1}{5}+\frac{x+1}{6}\)
2) \(\frac{x+1}{2009}+\frac{x+2}{2008}+\frac{x+3}{2007}=\frac{x+10}{2000}+\frac{x+11}{1999}+\frac{x+12}{1998}\)