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a: \(\Leftrightarrow-\dfrac{720}{150}=-4.8< x< \dfrac{-63}{210}=-0.3\)
mà x là số nguyên
nen \(x\in\left\{-4;-3;-2;-1\right\}\)
b: \(\Leftrightarrow-\dfrac{125}{27}< x< \dfrac{120}{210}=\dfrac{4}{7}\)
mà x là số nguyên
nên \(x\in\left\{-4;-3;-2;-1;0\right\}\)
A=\(\dfrac{2}{7}+\dfrac{-3}{8}+\dfrac{11}{7}+\dfrac{1}{3}+\dfrac{1}{7}+\dfrac{5}{-3}\)
A=\(\left(\dfrac{2}{7}+\dfrac{11}{7}+\dfrac{1}{7}\right)+\left(\dfrac{1}{3}+\dfrac{5}{-3}\right)+\dfrac{-3}{8}\)
A=\(2+\dfrac{-4}{3}+\dfrac{-3}{8}\)
A=\(\dfrac{7}{24}\)
B=\(\left(\dfrac{3}{17}+\dfrac{14}{17}\right)+\left(\dfrac{-18}{35}+\dfrac{17}{-35}\right)+\left(\dfrac{-5}{13}+\dfrac{-8}{13}\right)\)
B=\(\dfrac{17}{17}+\dfrac{-35}{35}+\dfrac{-13}{13}\)
B=\(1+\left(-1\right)+\left(-1\right)=-1\)
C=\(\dfrac{-3}{17}+\left(\dfrac{2}{3}+\dfrac{3}{17}\right)\)
C=\(\dfrac{-3}{17}+\dfrac{2}{3}+\dfrac{3}{17}=\left(\dfrac{-3}{17}+\dfrac{3}{17}\right)+\dfrac{2}{3}\)
C=0+\(\dfrac{2}{3}=\dfrac{2}{3}\)
D=\(\left(\dfrac{-1}{6}+\dfrac{5}{-12}\right)+\dfrac{7}{12}\)
D=\(\dfrac{-1}{6}+\dfrac{5}{-12}+\dfrac{7}{12}\)
D=\(\dfrac{-2}{12}+\dfrac{-5}{12}+\dfrac{7}{12}=\left(\dfrac{-2}{12}+\dfrac{-5}{12}\right)+\dfrac{7}{12}\)
D=\(\dfrac{-7}{12}+\dfrac{7}{12}=0\)
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a: \(\Leftrightarrow70+18< x< 120+126+70\)
=>88<x<316
hay \(x\in\left\{89;90;...;315\right\}\)
b: \(\Leftrightarrow-\dfrac{9}{3}< x< \dfrac{8}{5}+\dfrac{9}{5}=\dfrac{17}{5}\)
=>-3<x<3,4
hay \(x\in\left\{-2;-1;0;1;2;3\right\}\)
a,\(\dfrac{3}{7}\).\(\dfrac{14}{5}\)=\(\dfrac{6}{5}\)
b,\(\dfrac{35}{9}\).\(\dfrac{81}{7}\)=45
c,\(\dfrac{28}{17}\).\(\dfrac{68}{14}\)=8
d,\(\dfrac{35}{46}\).\(\dfrac{23}{105}\)=\(\dfrac{1}{6}\)
e,\(\dfrac{12}{5}\):\(\dfrac{16}{15}\)=\(\dfrac{12}{5}\).\(\dfrac{15}{16}\)=\(\dfrac{9}{4}\)
i,\(\dfrac{9}{8}\):\(\dfrac{6}{5}\)=\(\dfrac{9}{8}\).\(\dfrac{5}{6}\)=\(\dfrac{15}{16}\)
a: (x+1/2)(2/3-2x)=0
=>x+1/2=0 hoặc 2/3-2x=0
=>x=-1/2 hoặc x=1/3
b: 
c: \(\Leftrightarrow x\cdot\left(\dfrac{13}{4}-\dfrac{7}{6}\right)=\dfrac{5}{12}+\dfrac{5}{3}=\dfrac{5}{12}+\dfrac{20}{12}=\dfrac{25}{12}\)
\(\Leftrightarrow x=\dfrac{25}{12}:\dfrac{39-14}{12}=\dfrac{25}{25}=1\)
Ta có :\(\dfrac{1}{5}< \dfrac{1}{4};\dfrac{1}{6}< \dfrac{1}{4};\dfrac{1}{7}< \dfrac{1}{4};\dfrac{1}{8}< \dfrac{1}{4}\)
\(\Rightarrow\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+...+\dfrac{1}{8}< \dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}=\dfrac{4}{4}=1\left(1\right)\)
Ta có :\(\dfrac{1}{9}< \dfrac{1}{8};\dfrac{1}{10}< \dfrac{1}{8};\dfrac{1}{11}< \dfrac{1}{8};...;\dfrac{1}{17}< \dfrac{1}{8}\)
\(\Rightarrow\dfrac{1}{9}+\dfrac{1}{10}+\dfrac{1}{11}+...+\dfrac{1}{17}< \dfrac{1}{8}+\dfrac{1}{8}+\dfrac{1}{8}+...+\dfrac{1}{8}=\dfrac{8}{8}=1\left(2\right)\)
Từ (1) và (2)\(\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+...+\dfrac{1}{17}< 1+1=2\)
Vậy \(\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+...+\dfrac{1}{17}< 2\)
Ta có : \(\dfrac{1}{5}=\dfrac{1}{5}\), \(\dfrac{1}{6}< \dfrac{1}{5}\), \(\dfrac{1}{7}< \dfrac{1}{5}\),...,\(\dfrac{1}{9}< \dfrac{1}{5}\)
Vậy \(\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{9}< \dfrac{1}{5}\cdot5=1\)
\(\dfrac{1}{10}< \dfrac{1}{8},\dfrac{1}{11}< \dfrac{1}{8},...,\dfrac{1}{17}< \dfrac{1}{8}\)
Vậy \(\dfrac{1}{10}+\dfrac{1}{11}+...+\dfrac{1}{17}< \dfrac{1}{8}\cdot8=1\)
Vậy \(\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{17}< 1+1=2\)
Chúc các bạn học tốt
Ta có :
\(\dfrac{-6}{7}+\dfrac{2}{5}=\dfrac{\left(-30\right)+14}{35}=\dfrac{-16}{35}\)
\(\dfrac{-3}{105}+\dfrac{17}{35}=\dfrac{1+17}{35}=\dfrac{18}{35}\)
\(\Rightarrow-16< 7x< 18\)
\(\Rightarrow7x\in\left\{-14;14;7;-7;0\right\}\)
\(\Rightarrow x\in\left\{-2;2;1;-1;0\right\}\)
Vậy \(x\in\left\{-2;2;1;-1;0\right\}\)