Bài 1:

a, \(\frac{2}{5}< \frac{x}{5}< \frac{6}{5}\) => \(x\in\left\{3;4;5\right\}\)

b, \(-\frac{13}{9}< \frac{x}{72}< -\frac{11}{8}\)

=> \(-\frac{104}{72}< \frac{x}{72}< -\frac{99}{72}\)

=> \(x\in\left\{-103;-102;-101;-100\right\}\)

Bài 2:

a, \(\frac{2500}{6}m^2\) và 75dm²

Ta có: \(\frac{2500}{6}m^2=\frac{1250}{3}m^2=\frac{1250}{3}\cdot100=\frac{125000}{3}dm^2\)

\(75dm^2=\frac{225}{3}dm^2\)

mà \(\frac{125000}{3}dm^2>\frac{225}{3}dm^2\) => \(\frac{2500}{6}m^2>75dm^2\)

b, \(7dm\) và \(\frac{4}{5}m\)

Ta có: \(\frac{4}{5}m=8dm\)

mà 8dm > 7dm

=> \(7dm< \frac{4}{5}m\)

a)\(\frac{-5}{6}\).\(\frac{120}{25}\)<x<\(\frac{-7}{15}\).\(\frac{9}{14}\)

       -4                 <x<\(\frac{-3}{10}\)

\(\frac{-40}{10}\)<      x   <\(\frac{-3}{10}\)=>x E {-39:-38:-37:.....:-4}

b)\(\left(\frac{-5}{3}\right)^3\)<x<\(\frac{-24}{35}.\frac{-5}{6}\)

\(\frac{-875}{189}< x< \frac{108}{189}\)

=> x  E {\(\frac{-874}{189},\frac{-873}{189},......,\frac{107}{189}\)}

a) \(\left(x+\frac{1}{4}\right)^2+\frac{11}{25}=\frac{18}{25}\)

\(\Rightarrow\left(x+\frac{1}{4}\right)^2=\frac{7}{25}\)

\(\Rightarrow\) Không có x

\(\left(\frac{x}{10}-\frac{2}{3}\right)^2-\frac{1}{25}=0\)

\(\Leftrightarrow\left(\frac{x}{10}-\frac{2}{3}\right)^2=\frac{1}{25}\)

\(\Leftrightarrow\left(\frac{x}{10}-\frac{2}{3}\right)^2=\left(\pm\frac{1}{5}\right)^2\)

\(\Leftrightarrow\orbr{\begin{cases}\frac{x}{10}-\frac{2}{3}=\frac{1}{5}\\\frac{x}{10}-\frac{2}{3}=-\frac{1}{5}\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{26}{3}\\x=\frac{14}{3}\end{cases}}\)

\(\frac{5}{8}< \frac{4}{x}< \frac{5}{7}\)

\(\frac{5}{8}\cdot\frac{4}{4}< \frac{4}{x}\cdot\frac{5}{5}< \frac{5}{7}\cdot\frac{4}{4}\)

\(\frac{20}{32}< \frac{20}{5x}< \frac{20}{28}\)

\(\Rightarrow\frac{20}{32}< \frac{20}{30}< \frac{20}{28}\)

\(5x=30\)

\(x=6\)

Bài 3 

\(\frac{x-1}{9}=\frac{8}{3}\)

\(\Rightarrow\left(x-1\right).3=8.9\)

\(\Rightarrow\left(x-1\right).3=72\)

\(\Rightarrow x-1=24\)

\(\Rightarrow x=25\)

\(\frac{-x}{4}=\frac{-9}{x}\)

\(\Rightarrow\left(-x\right).x=\left(-9\right).4\)

\(\Rightarrow-x=-36\)

\(\Rightarrow x=36\)

\(\frac{x}{4}=\frac{18}{x+1}\)

\(\Rightarrow x.\left(x+1\right)=4.18\)

\(\Rightarrow x.\left(x+1\right)=72\)

Vì x và x + 1 là 2 số tự nhiên liên tiếp 

\(\Rightarrow x\left(x+1\right)=8.9\)

\(\Rightarrow\orbr{\begin{cases}x=8\\x=8\end{cases}}\)

Bài 4

\(\frac{x-4}{y-3}=\frac{4}{3},x-y=5\)

Ta có :

\(x-y=5\)

\(\Rightarrow x=5+y\)

\(\Rightarrow\frac{y+5-4}{y-3}=\frac{4}{3}\)

\(\Rightarrow\frac{y+1}{y-3}=\frac{4}{3}\)\(\)

\(\Rightarrow\left(y+1\right).3=\left(y-3\right).4\)

\(\Rightarrow y.3+1.3=y.4-3.4\)

\(\Rightarrow y.3+3=y.4-12\)

\(\Rightarrow y.3-y.4=-12-3\)

\(\Rightarrow-1y=-15\)

\(\Rightarrow y=\left(-15\right):\left(-1\right)\)

\(\Rightarrow y=15\)

Vì x = y + 5

\(\Rightarrow x=15+4\)

\(\Rightarrow x=19\)

Vậy x = 19 , y = 15

\(\frac{-x}{4}=\frac{-9}{x}\)

\(\Rightarrow\left(-x\right).x=4.\left(-9\right)\)

\(\Rightarrow-x=-9;x=4\)

\(\Rightarrow x=9;x=4\)