Đáp án:

 $6) x=\dfrac{2}{3}\\
7)
 {\left[\begin{aligned}x=\dfrac{22}{7}\\x=\dfrac{20}{7}\end{aligned}\right.}\\
8)
  {\left[\begin{aligned}x=\dfrac{17}{2}\\x=\dfrac{11}{2}\end{aligned}\right.}\\
9)
 {\left[\begin{aligned}x=\dfrac{-7}{6}\\x=\dfrac{-5}{6}\end{aligned}\right.}\\
10) {\left[\begin{aligned}x=\dfrac{88}{21}\\x=\dfrac{80}{21}\end{aligned}\right.}\\$

Giải thích các bước giải:

 $6) 1\dfrac{8}{35}-1\dfrac{1}{5}x=\dfrac{3}{7}\\
\Leftrightarrow \dfrac{43}{35}-\dfrac{6}{5}x=\dfrac{3}{7}\\
\Leftrightarrow \dfrac{6}{5}x=\dfrac{43}{35}-\dfrac{3}{7}\\
\Leftrightarrow \dfrac{6}{5}x=\dfrac{43}{35}-\dfrac{15}{35}\\
\Leftrightarrow \dfrac{6}{5}x=\dfrac{28}{35}=\dfrac{4}{5}\\
\Leftrightarrow x=\dfrac{4}{5}.\dfrac{5}{6}=\dfrac{2}{3}\\
7)
5|x-3|=\dfrac{5}{7}\\
\Leftrightarrow |x-3|=\dfrac{5}{7}:5=\dfrac{1}{7}\\
\Leftrightarrow {\left[\begin{aligned}x-3=\dfrac{1}{7}\\x-3=\dfrac{-1}{7}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{1}{7}+3\\x=\dfrac{-1}{7}+3\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{1}{7}+\dfrac{21}{7}\\x=\dfrac{-1}{7}+\dfrac{21}{7}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{22}{7}\\x=\dfrac{20}{7}\end{aligned}\right.}\\
8)
-\dfrac{3}{7}|x-7|=\dfrac{-9}{14}\\
\Leftrightarrow |x-7|=\dfrac{-9}{14}.\dfrac{-7}{3}\\
\Leftrightarrow |x-7|=\dfrac{3}{2}\\
\Leftrightarrow  {\left[\begin{aligned}x-7=\dfrac{3}{2}\\x-7=\dfrac{-3}{2}\end{aligned}\right.}\\
\Leftrightarrow  {\left[\begin{aligned}x=\dfrac{3}{2}+7\\x=\dfrac{-3}{2}+7\end{aligned}\right.}\\
\Leftrightarrow  {\left[\begin{aligned}x=\dfrac{3}{2}+\dfrac{14}{2}\\x=\dfrac{-3}{2}+\dfrac{14}{2}\end{aligned}\right.}\\
\Leftrightarrow  {\left[\begin{aligned}x=\dfrac{17}{2}\\x=\dfrac{11}{2}\end{aligned}\right.}\\
9)
|-x-1|=\dfrac{1}{6}\\
\Leftrightarrow {\left[\begin{aligned}-x-1=\dfrac{1}{6}\\-x-1=-\dfrac{1}{6}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}-x=\dfrac{1}{6}+1\\-x=-\dfrac{1}{6}+1\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}-x=\dfrac{1}{6}+\dfrac{6}{6}\\-x=-\dfrac{1}{6}+\dfrac{6}{6}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}-x=\dfrac{7}{6}\\-x=\dfrac{5}{6}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{-7}{6}\\x=\dfrac{-5}{6}\end{aligned}\right.}\\
10) |x-4|=\dfrac{1}{3}-\dfrac{1}{7}\\
\Leftrightarrow |x-4|=\dfrac{7}{21}-\dfrac{3}{21}\\
\Leftrightarrow |x-4|=\dfrac{4}{21}\\
\Leftrightarrow {\left[\begin{aligned}x-4=\dfrac{4}{21}\\x-4=-\dfrac{4}{21}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{4}{21}+4\\x=-\dfrac{4}{21}+4\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{4}{21}+\dfrac{84}{21}\\x=-\dfrac{4}{21}+\dfrac{84}{21}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{88}{21}\\x=\dfrac{80}{21}\end{aligned}\right.}\\$