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a)\(\frac{5}{21}\)+\(\frac{-3}{7}\)<\(\frac{x}{21}\)<\(\frac{-2}{7}\)+\(\frac{8}{21}\)
\(\Rightarrow\)\(\frac{-4}{21}\)<\(\frac{x}{21}\)<\(\frac{2}{21}\)
\(\Rightarrow\)\(\frac{x}{21}\)\(\in\)\(\left\{\frac{-3}{21};\frac{-2}{21};\frac{-1}{21};\frac{0}{21};\frac{1}{21}\right\}\)
vậy x\(\in\)\(\left\{-3;-2;-1;0;1\right\}\)
a) \(\frac{1}{3}+\frac{3}{35}< \frac{x}{210}< \frac{7}{7}+\frac{3}{5}+\frac{1}{3}\)
\(\Rightarrow\frac{44}{105}< \frac{x}{210}< \frac{29}{15}\)
\(\Rightarrow\frac{88}{210}< \frac{x}{210}< \frac{406}{210}\)
\(\Rightarrow x\in\left\{89;90;91;...;405\right\}\)
b) \(\frac{5}{3}+-\frac{14}{3}< x< \frac{8}{5}+\frac{8}{10}\)
\(\Rightarrow-3< x< 2\frac{2}{5}\)
=> x thuộc {-2;-1;0;1;2} ( nếu x là số nguyên)
5/3+ -14/3<x<8/5+18/10
=>-9/3<x<17/5
=> -3<x<3,4
Vi x la so nguyen=> x la -2,-1,0,1,2
5/3 + -14/3 < x < 8/5 + 18/10
=> -9/3 < x < 16/10 + 18/10
=> -3 < x < 34/10
=> -3 < x < 3 , 4
=> x thuộc { -2 , -1 , 0 , 1 , 2 , 3 }
Chúc học tốt !!!! ^_^
\(\frac{x}{7}=\frac{x+1}{14}\Leftrightarrow14x=7x+7\Leftrightarrow7x=7\Leftrightarrow x=1\)
\(\frac{1}{2}+\frac{1}{3}+\frac{1}{6}\le x\le\frac{15}{4}+\frac{18}{8}\)
\(\Leftrightarrow1\le x\le6\Leftrightarrow x=1;2;3;4;5;6\)
\(\frac{1}{2}+\frac{-3}{5}+\frac{1}{10}\le x\le\frac{8}{3}+\frac{14}{6}\)
\(\Leftrightarrow\frac{1}{2}-\frac{3}{5}+\frac{1}{10}\le x\le\frac{8}{3}+\frac{14}{6}\)
\(\Leftrightarrow0\le x\le5\Leftrightarrow x=0;1;2;3;4;5\)
\(\frac{x}{7}=\frac{x+1}{14}\)
=> \(\frac{x\cdot2}{7\cdot2}=\frac{x+1}{14}\)
=> \(2x=x+1\)
=> \(2x-x-1=0\)
=> \(1x-1=0\)
=> \(x=1\)
\(\frac{1}{2}+\frac{1}{3}+\frac{1}{6}\le x\le\frac{15}{4}+\frac{18}{8}\)
=> \(1\le x\le6\)
=> \(x=\left\{1;2;3;4;5;6\right\}\)
\(\frac{1}{2}+\frac{-3}{5}+\frac{1}{10}\le x\le\frac{8}{3}+\frac{14}{6}\)
=> \(0\le x\le5\)
=> \(x=\left\{0;1;2;3;4;5\right\}\)
<=>-3<x<17/5
<=>-3<x<3,4
Vì x thuộc Z
=>x=(-2;-1;0;1;2;3)
k nha