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a)\(\frac{7}{11}< x-\frac{1}{7}< \frac{10}{3}\)
\(=>\frac{7}{11}+\frac{1}{7}< x< \frac{10}{3}+\frac{1}{7}\)
\(=>\frac{60}{77}< x< \frac{73}{21}\)
VẬY \(\frac{60}{77}< x< \frac{73}{21}\)
b) \(\frac{40}{99}>x>\frac{43}{176}\)
\(\frac{x}{9}< \frac{4}{7}< \frac{x+1}{9}\)
=> \(\frac{7x}{63}< \frac{36}{63}< \frac{7x+7}{63}\)
=> 7x < 36 < 7x + 7
=> x = 5
Vậy x = 5
\(\frac{x+1}{29}+\frac{x+4}{13}=\frac{x+9}{7}\)
\(\Leftrightarrow\frac{x+1}{29}+1+\frac{x+4}{13}+2=\frac{x+9}{7}+3\)
\(\Leftrightarrow\frac{x+30}{29}+\frac{x+30}{13}=\frac{x+30}{7}\)
\(\Leftrightarrow\frac{x+30}{29}+\frac{x+30}{13}-\frac{x+30}{7}=0\)
\(\Leftrightarrow\left(x+30\right)\left(\frac{1}{29}+\frac{1}{13}-\frac{1}{7}\right)=0\)
\(\Leftrightarrow x+30=0\)( vì \(\frac{1}{29}+\frac{1}{13}-\frac{1}{7}\ne0\))
\(\Leftrightarrow x=-30\)
Vậy...
\(\frac{x+1}{29}+\frac{x+4}{13}=\frac{x+9}{7}\)
\(\Leftrightarrow\frac{x+1}{29}+1+\frac{x+4}{13}+2=\frac{x+9}{7}+3\)
\(\Leftrightarrow\frac{x+30}{29}+\frac{x+30}{13}=\frac{x+30}{7}\)
\(\Leftrightarrow\frac{x+30}{29}+\frac{x+30}{13}-\frac{x+30}{7}=0\)
\(\Leftrightarrow\left(x+30\right)\left(\frac{1}{29}+\frac{1}{13}-\frac{1}{7}\right)=0\)
Vì \(\frac{1}{29}+\frac{1}{13}-\frac{1}{7}\ne0\)
Nên \(x+30=0\)
\(\Leftrightarrow x=-30\)
a: \(\Leftrightarrow\dfrac{-9}{11}< \dfrac{7}{a}< -\dfrac{9}{13}\)
\(\Leftrightarrow\dfrac{-63}{77}< \dfrac{-63}{-9a}< \dfrac{-63}{91}\)
=>77<-9a<91
=>-9a=81 hoặc -9a=90
=>a=-9 hoặc a=-10
b: Theo đề, ta có:
\(\dfrac{-3}{5}< \dfrac{9}{a}< \dfrac{-4}{9}\)
\(\Leftrightarrow\dfrac{-36}{60}< \dfrac{36}{4a}< \dfrac{-36}{54}\)
=>4a=-56
hay a=-14
#)Giải :
Ta có : \(\frac{9}{13}< \frac{7}{x}< \frac{9}{11}\)
\(\Leftrightarrow\frac{63}{91}< \frac{63}{9x}< \frac{63}{77}\)
\(\Leftrightarrow91< 9x< 77\)
\(\Leftrightarrow x\in\left\{9;10\right\}\)
Vậy các phân số cần tìm là \(\frac{7}{9};\frac{7}{10}\)
9/13 < 7/x < 9/11
=> 63/91 < 63/9x < 63/77
=> 91 > 7x > 77
=> x = 9 hoặc = 10
vậy_