\(a,\dfrac{x}{5}=\dfrac{-18}{10}\\ \Rightarrow x=-\dfrac{18}{10}.5\\ \Rightarrow x=-9\\ b,\dfrac{6}{x-1}=\dfrac{-3}{7}\\ \Rightarrow6.7=-3\left(x-1\right)\\ \Rightarrow42=-3x+3\\ \Rightarrow42+3x-3=0\\ \Rightarrow3x+39=0\\ \Rightarrow3x=-39\\ \Rightarrow x=-13\\ c,\dfrac{y-3}{12}=\dfrac{3}{y-3}\\ \Rightarrow\left(y-3\right)^2=36\\ \Rightarrow\left[{}\begin{matrix}y-2=6\\y-2=-6\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}y=8\\y=-4\end{matrix}\right.\)

\(d,\dfrac{x}{25}=\dfrac{-5}{x^2}\\ \Rightarrow x^3=-125\\ \Rightarrow x^3=\left(-5\right)^3\\ \Rightarrow x=-5\)

\(a,\left(x-\dfrac{5}{8}\right)\cdot\dfrac{8}{18}=-\dfrac{15}{16}\\ x-\dfrac{5}{8}=-\dfrac{15}{36}:\dfrac{8}{18}\\ x-\dfrac{5}{8}=-\dfrac{15}{16}\\ x=-\dfrac{15}{16}+\dfrac{5}{8}\\ x=-\dfrac{15}{16}+\dfrac{10}{16}\\ x=-\dfrac{5}{16}\\ b,x-\dfrac{1}{3}=\dfrac{5}{6}\\ x=\dfrac{5}{6}+\dfrac{1}{3}\\ x=\dfrac{5}{6}+\dfrac{2}{6}\\ x=\dfrac{7}{6}\)

\(a,\left(x-\dfrac{5}{8}\right).\dfrac{5}{8}=-\dfrac{15}{36}\)

\(\left(x-\dfrac{5}{8}\right)=-\dfrac{15}{36}\div\dfrac{5}{8}\)

\(x-\dfrac{5}{8}=-\dfrac{2}{3}\)

\(x=-\dfrac{2}{3}+\dfrac{5}{8}\)

\(x=-\dfrac{1}{24}\)

\(b,\left(x-\dfrac{1}{3}\right)=\dfrac{5}{6}\)

\(\Rightarrow x-\dfrac{1}{3}=\dfrac{5}{6}\)

\(x=\dfrac{5}{6}+\dfrac{1}{3}\)

\(x=\dfrac{7}{6}\)

\(a)\left(x-\dfrac{5}{8}\right).\dfrac{5}{18}=-\dfrac{15}{36}\)

    \(\left(x-\dfrac{5}{8}\right).\dfrac{5}{18}=\dfrac{-5}{12}\) 

     \(\left(x-\dfrac{5}{8}\right)\)       \(=\dfrac{-5}{12}\div\dfrac{5}{18}=\dfrac{-3}{2}\)

        \(x\)                 \(=\left(\dfrac{-3}{2}\right)+\dfrac{5}{8}=\dfrac{-7}{8}\)

\(b)\left(x-\dfrac{1}{3}\right)=\dfrac{5}{6}\)

      \(x\)            \(=\dfrac{5}{6}+\dfrac{1}{3}\)

      \(x\)            \(=\dfrac{7}{6}\)

\(\left\{\dfrac{-5< 0< -0,4}{x\in Z}\right\}\Rightarrow x\in\left\{-4;-3;-2;-1\right\}\)

chiu thôi leo nheo qua

chịu không viết được hỗn số

\(\dfrac{-9}{7}+\dfrac{5}{-7}< x\le\dfrac{-5}{2}+\dfrac{18}{4}\)

\(\dfrac{-9}{7}+\dfrac{-5}{7}< x\le\dfrac{10}{4}+\dfrac{18}{4}\)

\(\dfrac{-14}{7}< x\le2\)

\(-2< x\le2\)

\(\Rightarrow\)\(x=\left\{-1;0;1;2\right\}\)

-2<-1,0,1,2<2

a) \(\dfrac{x-4}{15}=\dfrac{5}{3}\)

\(\Leftrightarrow x-4=15.\dfrac{5}{3}\)

\(\Leftrightarrow x-4=25\)

\(\Leftrightarrow x=29\) thỏa \(x\inℤ\)

b) \(\dfrac{x}{4}=\dfrac{18}{x+1}\left(x\ne-1\right)\)

\(\Leftrightarrow x\left(x+1\right)=18.4\)

\(\Leftrightarrow x\left(x+1\right)=72\)

vì \(72=8.9=\left(-8\right).\left(-9\right)\)

\(\Leftrightarrow x\in\left\{8;-9\right\}\left(x\inℤ\right)\)

c) \(2x+3⋮x+4\) \(\left(x\ne-4;x\inℤ\right)\)

\(\Leftrightarrow2x+3-2\left(x+4\right)⋮x+4\)

\(\Leftrightarrow2x+3-2x-8⋮x+4\)

\(\Leftrightarrow-5⋮x+4\)

\(\Leftrightarrow x+4\in\left\{-1;1;-5;5\right\}\)

\(\Leftrightarrow x\in\left\{-5;-3;-9;1\right\}\)

\(a,\dfrac{5}{13}\times\dfrac{4}{15}\times13=\dfrac{5\times4\times13}{13\times5\times3}=\dfrac{4}{3}\\ b,\left(\dfrac{3}{7}+\dfrac{5}{2}\right)\times\dfrac{7}{5}=\dfrac{3}{7}\times\dfrac{7}{5}+\dfrac{5}{2}\times\dfrac{7}{5}=\dfrac{3}{5}+\dfrac{7}{2}=\dfrac{6}{10}+\dfrac{35}{10}=\dfrac{41}{10}\\ c,\dfrac{1}{5}\times\dfrac{11}{18}+\dfrac{11}{18}\times\dfrac{3}{5}=\dfrac{11}{18}\times\left(\dfrac{1}{5}+\dfrac{3}{5}\right)=\dfrac{11}{18}\times\dfrac{4}{5}=\dfrac{22}{45}\)

a, 4/3  b, 41/10   c,22/45

Giải:

a) \(\dfrac{-1}{5}\le\dfrac{x}{8}\le\dfrac{1}{4}\) 

\(\Rightarrow\dfrac{-8}{40}\le\dfrac{5x}{40}\le\dfrac{10}{40}\) 

\(\Rightarrow5x\in\left\{0;\pm5;10\right\}\) 

\(\Rightarrow x\in\left\{0;\pm1;2\right\}\) 

b) \(\dfrac{4}{x-6}=\dfrac{y}{24}=\dfrac{-12}{18}\) 

\(\Rightarrow\dfrac{4}{x-6}=\dfrac{-12}{18}\) 

\(\Rightarrow-12.\left(x-6\right)=4.18\) 

\(\Rightarrow-12x+72=72\) 

\(\Rightarrow-12x=72-72\) 

\(\Rightarrow-12x=0\) 

\(\Rightarrow x=0:-12\) 

\(\Rightarrow x=0\) 

\(\Rightarrow\dfrac{y}{24}=\dfrac{-12}{18}\) 

\(\Rightarrow y=\dfrac{-12.24}{18}=-16\) 

c) \(\dfrac{x+46}{20}=x.\dfrac{2}{5}\) 

\(\dfrac{x+46}{20}=\dfrac{2x}{5}\) 

\(\Rightarrow5.\left(x+46\right)=2x.20\) 

\(\Rightarrow5x+230=40x\) 

\(\Rightarrow5x-40x=-230\) 

\(\Rightarrow-35x=-230\) 

\(\Rightarrow x=-230:-35\) 

\(\Rightarrow x=\dfrac{46}{7}\) 

Chúc bạn học tốt!

X + X x \(\dfrac{1}{3}\) + \(\dfrac{5}{18}\) = \(\dfrac{7}{6}\)

X x \(\dfrac{4}{3}\)                 = \(\dfrac{7}{6}-\dfrac{5}{18}\)

X x \(\dfrac{4}{3}\)                 = \(\dfrac{8}{9}\)

X                        = \(\dfrac{8}{9}:\dfrac{4}{3}=\dfrac{2}{3}\)                  

\(x\cdot\left(\dfrac{1}{3}+1\right)=\dfrac{21}{18}-\dfrac{5}{18}=\dfrac{16}{18}=\dfrac{8}{9}\)

\(x=\dfrac{8}{9}:\dfrac{4}{3}=\dfrac{8}{9}\cdot\dfrac{3}{4}=\dfrac{4\cdot2\cdot3}{3\cdot3\cdot4}=\dfrac{2}{3}\)