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\(\frac{x+1}{10}+\frac{x+1}{11}=\frac{x+1}{12}\)
=> \(\frac{x+1}{10}+\frac{x+1}{11}-\frac{x+1}{12}=0\)
⇒ \(\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}-\frac{1}{12}\right)=0\)
⇒ \(x+1=0\) (do \(\left(\frac{1}{10}+\frac{1}{11}-\frac{1}{12}\right)\ne0\)
=> x = - 1
\(\frac{1}{2}x-\frac{1}{6}x+1=0\)
=> \(x\left(\frac{3}{6}-\frac{1}{6}\right)=-1\)
=> \(\frac{1}{3}x=-1\)
=> \(x=-3\)
#)Giải :
a) x + 2x + 3x + ... + 100x = - 213
=> 100x + ( 2 + 3 + 4 + ... + 100 ) = - 213
=> 100x + 5049 = - 213
<=> 100x = - 5262
<=> x = - 52,62
#)Giải :
b) \(\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}x-\frac{1}{6}\)
\(\Rightarrow\frac{1}{2}x+\frac{1}{4}x=\frac{1}{3}+\frac{1}{6}\)
\(\Rightarrow\frac{1}{2}x+\frac{1}{4}x=\frac{1}{2}\)
\(\Rightarrow\left(\frac{1}{2}+\frac{1}{4}\right)x=\frac{1}{2}\)
\(\Rightarrow\frac{3}{4}x=\frac{1}{2}\)
\(\Leftrightarrow x=\frac{2}{3}\)
= (x + 1) (1/10 + 1/11 + 1/12 + 1/13 + 1/14 ) = 0
=> x + 1 = 0
=> x = - 1
a) \(\frac{x+1}{3}=\frac{x-2}{4}\)
=> (x+1).4 = (x - 2) . 3
=> 4x + 4 = 3x - 6
=> 4x - 3x = - 6 - 4
=> x = - 10
b) \(\frac{x-6}{7}+\frac{x-7}{8}+\frac{x-8}{9}=\frac{x-9}{10}+\frac{x-10}{11}+\frac{x-11}{12}\)
\(\Rightarrow\left(\frac{x-6}{7}+1\right)+\left(\frac{x-7}{8}+1\right)+\left(\frac{x-8}{9}+1\right)=\left(\frac{x-9}{10}+1\right)+\left(\frac{x-10}{11}+1\right)+\left(\frac{x-11}{12}+1\right)\)
\(\Rightarrow\frac{x+1}{7}+\frac{x+1}{8}+\frac{x+1}{9}=\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}\)
\(\Rightarrow\frac{x+1}{7}+\frac{x+1}{8}+\frac{x+1}{9}-\frac{x+1}{10}-\frac{x+1}{11}-\frac{x+1}{12}\) = 0
\(\Rightarrow\left(x+1\right).\left(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}-\frac{1}{11}-\frac{1}{12}\right)\)
Vì \(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}-\frac{1}{11}-\frac{1}{12}\ne0\) nên x + 1 =0
=> x = -1
c) Xem lại đề
\(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=0\)
\(=>\left\{{}\begin{matrix}\frac{x+1}{10}=0\\\frac{x+1}{11}=0\\\frac{x+1}{12}=0\end{matrix}\right.=>x+1=0\)
=> x = 0 - 1
=> x = -1
\(\frac{x+1}{10}+\frac{x+2}{10}=0\)
\(\frac{x+1+x+2}{10}=0\)
\(\frac{2x+3}{10}=0\)
\(2x+3=0\)
\(2x=-3\)
\(\Rightarrow x=-\frac{3}{2}\)
\(\frac{x+1}{10}+\frac{x+2}{10}=0\)
\(\Rightarrow\frac{x+1}{10}=0\) và \(\frac{x+2}{10}=0\)
\(\Rightarrow x+1=0\) và \(x+2=0\)
\(\Rightarrow x=-1\) và \(x=-2\)
tíc mình nha