Tim x : \(\frac{7}{11}< x-\frac{1}{7}< \frac{10}{13}\)
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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
a/ \(\frac{15}{x}-\frac{1}{3}=\frac{28}{51}\)
\(\frac{15}{x}=\frac{28}{51}+\frac{1}{3}\)
\(\frac{15}{x}=\frac{15}{17}\)
\(x=15:\frac{15}{17}\)
\(x=17\)
b) \(\frac{x}{20}-\frac{2}{5}=10\)
\(\frac{x}{20}=10+\frac{2}{5}\)
\(\frac{x}{20}=\frac{52}{5}\)
\(x=\frac{52}{5}\cdot20\)
\(x=208\)
c) \(x+\frac{18}{23}=2\frac{1}{3}\)
\(x+\frac{18}{23}=\frac{7}{3}\)
\(x=\frac{7}{3}-\frac{18}{23}\)
\(x=\frac{107}{69}\)
d) \(\frac{7}{11}< x-\frac{1}{7}< \frac{10}{13}\)
\(\Rightarrow\frac{7}{11}+\frac{1}{7}< x< \frac{10}{13}\)
\(\frac{60}{77}< x< \frac{60}{78}\)
Đến đây .....bí!
e) Tớ bỏ luôn đc ko.
D) 7/11<X-1/7<10/13
<=> 7/11+1/7<x< 10/13+1/7
<=> 60/77< x< 83/91
<=> 5460/1001 <x< 6391/1001
vậy X thuộc tập hợp các phÂN số lớn hơn 5460/1001 và bé hơn 913/1001
vd : Y/1001 trong đó y là 5461;5462;5463...6389;6390
\(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}+\frac{x+1}{14}=0\)
\(\left(x+1\right).\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)
vì \(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\)\(\ne\)0 nên x + 1 = 0 \(\Rightarrow\)x = -1
#)Giải :
a) x + 2x + 3x + ... + 100x = - 213
=> 100x + ( 2 + 3 + 4 + ... + 100 ) = - 213
=> 100x + 5049 = - 213
<=> 100x = - 5262
<=> x = - 52,62
#)Giải :
b) \(\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}x-\frac{1}{6}\)
\(\Rightarrow\frac{1}{2}x+\frac{1}{4}x=\frac{1}{3}+\frac{1}{6}\)
\(\Rightarrow\frac{1}{2}x+\frac{1}{4}x=\frac{1}{2}\)
\(\Rightarrow\left(\frac{1}{2}+\frac{1}{4}\right)x=\frac{1}{2}\)
\(\Rightarrow\frac{3}{4}x=\frac{1}{2}\)
\(\Leftrightarrow x=\frac{2}{3}\)
\(3x.\left(x-\frac{2}{3}\right)=0\)
\(\Leftrightarrow3x=0\)hoặc \(x-\frac{2}{3}=0\)
\(3x=0\Rightarrow x=0\)
\(x-\frac{2}{3}=0\Rightarrow x=0+\frac{2}{3}=\frac{2}{3}\)
Vậy..