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Theo đầu bài ta có:
\(A=\frac{1}{5\cdot8}+\frac{1}{8\cdot11}+...+\frac{1}{x\left(x+3\right)}=\frac{1}{6}\)
\(\Rightarrow3A=\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+...+\frac{3}{x\left(x+3\right)}=\frac{1}{6}\)
\(3A=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{x}-\frac{1}{x+3}=\frac{1}{6}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{x+3}=\frac{1}{6}\)
\(\frac{1}{x+3}=\frac{1}{5}-\frac{1}{6}\)
\(x+3=1:\frac{1}{30}\)
\(x=30-3\)
\(x=27\)
\(\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{x.\left(x+3\right)}=\frac{1}{6}\)
\(\Rightarrow3.\left(\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{x.\left(x+3\right)}\right)=\frac{3}{6}\)
\(\Rightarrow\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{x\left(x+3\right)}=\frac{1}{2}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{x}-\frac{1}{x+3}=\frac{1}{2}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{x+3}=\frac{1}{2}\)
\(\Rightarrow\frac{1}{x+3}=\frac{1}{5}-\frac{1}{2}=-\frac{3}{10}\Rightarrow-3.\left(x+3\right)=10\)
=>-3x-9=10
=>-3x=19
=>x=-19/3
Bài 1:
Ta có: \(4-2\left(x+1\right)=2\)
\(\Leftrightarrow2\left(x+1\right)=2\)
\(\Leftrightarrow x+1=1\)
hay x=0
Bài 2:
Ta có: \(\left|2x-3\right|-1=2\)
\(\Leftrightarrow\left|2x-3\right|=3\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=3\\2x-3=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=6\\2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=0\end{matrix}\right.\)
a) \(\frac{X}{2}-\frac{11}{5}=\frac{7}{8}\cdot\frac{64}{49}\)
\(\Rightarrow\frac{x}{2}-\frac{11}{5}=\frac{8}{7}\)
\(\Rightarrow\frac{x}{2}=\frac{8}{7}+\frac{11}{5}\)
\(\Rightarrow\frac{x}{2}=\frac{117}{35}\)\(\Rightarrow x=\frac{117}{35}\cdot2=\frac{234}{35}\)
b)\(\frac{x}{5}+\frac{9}{2}=\frac{6}{7}\cdot\frac{36}{49}\)
\(\Rightarrow\frac{x}{5}+\frac{9}{2}=\frac{216}{343}\)
\(\Rightarrow\frac{x}{5}=\frac{216}{343}-\frac{9}{2}=\frac{-2655}{686}\)
\(\Rightarrow x=\frac{-2655}{686}\cdot5=\frac{-13275}{686}\)
x/2 - 11/5 = 7/8 . 64/49
x/2 - 11/5 = 8/7
x/2 =8/7 + 11/5
x/2 = 117/35
x = 2.117/35 ( tính chất phân số bằng nhau)
x = 234/35
x/5 + 9/2 = 6/7 . 36/49
x/5 + 9/2 = 216/343
x/5 = 216/343 - 9/2
x/5 = -2655/686
x = 5.(-2655)/686
x = -13275/686
1.
a, => 21-x+3 < 0
=> 24-x < 0
=> x < 24
b, => 7+x > 0
=> x > -7
c, => x-1 < 0 ; x+2 > 0 ( vì x-1 < x+2 )
=> x < 1 ; x > -2
=> -2 < x < 1
Tk mk nha
Mình nghĩ bạn chép sai đề rồi. Hãy kiểm tra và sửa lại đề nhé
a)\(\frac{5}{3}-\frac{2}{3}\times x=1\)
=>\(\frac{2}{3}\times x=\frac{5}{3}-1\)
=>\(\frac{2}{3}\times x=\frac{2}{3}\)
=>\(x=\frac{2}{3}:\frac{2}{3}\)
=>\(x=1\)
b)\(\frac{1}{2}+\frac{5}{7}:x=\frac{1}{6}\)
=>\(\frac{5}{7}:x=\frac{1}{6}-\frac{1}{2}\)
=>\(\frac{5}{7}:x=-\frac{1}{3}\)
=>\(x=-\frac{1}{3}\times\frac{5}{7}\)
=>\(x=-\frac{5}{21}\)
\(x\) + \(\dfrac{3}{4}\)\(\times\) \(x\) = \(\dfrac{6}{-11}\) + \(\dfrac{-5}{2}\)
\(x\times\) (1 + \(\dfrac{3}{4}\)) = \(\dfrac{-67}{22}\)
\(x\) \(\times\) \(\dfrac{7}{4}\) = \(\dfrac{-67}{22}\)
\(x\) = \(\dfrac{-67}{22}\)
Vậy \(x=\) \(\dfrac{-67}{22}\)