\(\Rightarrow\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}=0\)

Đặt x + 1 ra ngoài ta được:

\(\Rightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)

MÀ \(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\ne0\)

=> x + 1 = 0

=> x = 0 - 1 = -1 

Đặt \(\frac{13}{15}x-\left(\frac{15}{21}+x\right).\frac{7}{30}=0\)

\(\Leftrightarrow\frac{13}{15}x-\left(\frac{1}{6}+\frac{7}{30}x\right)=0\Leftrightarrow\frac{19}{30}x-\frac{1}{6}=0\Leftrightarrow x=\frac{5}{19}\)

Tương tự thôi 

a) \(\left(x-\frac{2}{5}\right).\left(x+\frac{3}{7}\right)<0\)

\(\Rightarrow x-\frac{2}{5}<0\)                      hoặc       \(x-\frac{2}{5}>0\)

      \(x+\frac{3}{7}>0\)                                     \(x+\frac{3}{7}<0\)

\(\Rightarrow x<\frac{2}{5}\)                               hoặc        \(x>\frac{2}{5}\)

      \(x>-\frac{3}{7}\)                                          \(x<-\frac{3}{7}\)

\(\Rightarrow-\frac{3}{7}                    hoặc         \(x\in rỗng\) 

vậy \(-\frac{3}{7}

b) \(\frac{1}{2}-\left(\frac{1}{3}+\frac{1}{4}\right)\le x\le\frac{1}{24}-\left(\frac{1}{8}-\frac{1}{3}\right)\)

\(\frac{-1}{12}\le x\le\frac{1}{4}\)

\(\frac{-1}{12}\le x\le\frac{3}{12}\)

\(\Rightarrow x=\frac{-1}{12};0;\frac{1}{12};\frac{2}{12};\frac{3}{12}\)

\(\frac{5}{6}x+\frac{1}{2}-\frac{1}{3}x=0.75x-\frac{7}{8}\)

\(\frac{5}{6}x-\frac{1}{3}x-\frac{3}{4}x=-\frac{7}{8}-\frac{1}{2}\)     ( 3/4x là 0,75x nha)

\(x\times\left(\frac{10}{12}-\frac{4}{12}-\frac{9}{12}\right)=-\frac{7}{8}-\frac{4}{8}\)

\(x\times\left(-\frac{3}{12}\right)=-\frac{11}{8}\Rightarrow x=\frac{11}{8}\div\left(-\frac{3}{12}\right)=-\frac{11}{2}\)

Bạn tham khảo ở đây nhé, mình làm rồi đấy: https://olm.vn/hoi-dap/detail/211418926066.html

\(\frac{3}{4}x-\frac{2}{3}.\left(\frac{3}{5}x-\frac{6}{5}\right)=\frac{1}{7}-\frac{2}{9}x\)

\(\frac{3}{4}x-\frac{2}{5}x+\frac{4}{5}=\frac{1}{7}-\frac{2}{9}x\)

\(\left(\frac{3}{4}-\frac{2}{5}\right)x+\frac{4}{5}=\frac{1}{7}-\frac{2}{9}x\)

\(\left(\frac{15}{20}-\frac{8}{20}\right)x+\frac{4}{5}=\frac{1}{7}-\frac{2}{9}x\)

\(\frac{7}{20}x+\frac{4}{5}=\frac{1}{7}-\frac{2}{9}x\)

\(\frac{1}{7}-\frac{4}{5}=\frac{2}{9}x-\frac{7}{20}x\)

\(\frac{5}{35}-\frac{28}{35}=\left(\frac{2}{9}-\frac{7}{20}\right)x\)

\(\frac{-23}{35}=\left(\frac{40}{180}-\frac{63}{180}\right)x\)

\(\frac{-23}{180}x=\frac{-23}{35}\)

\(x=\frac{-23}{35}:\frac{-23}{180}\)

\(x=\frac{-23}{35}.\frac{180}{-23}\)

\(x=\frac{180}{35}\)

Vậy \(x=\frac{180}{35}\)

Chúc bạn học tốt

                                                                                      Bài giải

\(\frac{2}{7}x+\frac{5}{9}=\frac{1}{2}x+\frac{3}{4}\)

\(\frac{2}{7}x-\frac{1}{2}x=\frac{3}{4}-\frac{5}{9}\)

\(-\frac{5}{14}x=\frac{7}{36}\)

\(x=\frac{7}{36}\text{ : }\frac{-5}{14}\)

\(x=-\frac{49}{90}\)

\(\frac{2}{7}x+\frac{5}{9}=\frac{1}{2}x+\frac{3}{4}\)

\(\frac{2}{7}x-\frac{1}{2}x=\frac{3}{4}-\frac{5}{9}\)

\(x.\left(\frac{2}{7}-\frac{1}{2}\right)=\frac{7}{36}\)

\(x.-\frac{3}{14}=\frac{7}{36}\)

\(x=\frac{7}{36}:-\frac{3}{14}\)

\(x=-\frac{49}{54}\)

vậy \(x=-\frac{49}{54}\)