Đáp án:

 $1)
a) x=\dfrac{-1}{2}\\
b) x=\dfrac{33}{24}\\
c) x=\dfrac{1}{9}$

v)${\left[\begin{aligned}x=\dfrac{5}{7}\\x=\dfrac{2}{7}\end{aligned}\right.}\\
2)
a) \dfrac{47}{144}\\
b)\dfrac{13}{10}$

Giải thích các bước giải:

1)
$a) \left ( 2x-\dfrac{1}{2} \right ).\dfrac{3}{7}=\dfrac{-9}{14}\\
\Leftrightarrow 2x-\dfrac{1}{2}=\dfrac{-9}{14}.\dfrac{7}{3}\\
\Leftrightarrow 2x=\dfrac{-3}{2}+\dfrac{1}{2}\\
\Leftrightarrow 2x=\dfrac{-2}{2}=-1\\
\Leftrightarrow x=\dfrac{-1}{2}\\
b) \dfrac{2}{3}x-\dfrac{1}{2}=\dfrac{5}{12}\\
\Leftrightarrow \dfrac{2}{3}x=\dfrac{5}{12}+\dfrac{1}{2}\\
\Leftrightarrow \dfrac{2}{3}x=\dfrac{5}{12}+\dfrac{6}{12}\\
\Leftrightarrow \dfrac{2}{3}x=\dfrac{11}{12}\\
\Leftrightarrow x=\dfrac{11}{12}.\dfrac{3}{2}=\dfrac{33}{24}\\
c) \dfrac{2}{5}x+\dfrac{1}{2}x=\dfrac{1}{10}\\
\Leftrightarrow \left ( \dfrac{2}{5}+\dfrac{1}{2} \right )x=\dfrac{1}{10}\\
\Leftrightarrow \left ( \dfrac{4}{10}+\dfrac{5}{10} \right )x=\dfrac{1}{10}\\
\Leftrightarrow \dfrac{9}{10}x=\dfrac{1}{10}\\
\Leftrightarrow x=\dfrac{1}{10}.\dfrac{10}{9}=\dfrac{1}{9}\\
v) \left | x-\dfrac{1}{2} \right |=\dfrac{3}{14}\\
\Leftrightarrow {\left[\begin{aligned}x-\dfrac{1}{2}=\dfrac{3}{14}\\x-\dfrac{1}{2}=\dfrac{-3}{14}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x\dfrac{3}{14}+\dfrac{1}{2}\\x=\dfrac{-3}{14}+\dfrac{1}{2}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x\dfrac{3}{14}+\dfrac{7}{14}\\x=\dfrac{-3}{14}+\dfrac{7}{14}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{10}{14}\\x=\dfrac{4}{14}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{5}{7}\\x=\dfrac{2}{7}\end{aligned}\right.}\\
2)
a) \left ( \dfrac{3}{8}-\dfrac{7}{12} \right ).\dfrac{5}{6}+\dfrac{1}{2}\\
=\left ( \dfrac{9}{24}-\dfrac{14}{24} \right ).\dfrac{5}{6}+\dfrac{1}{2}\\
=\dfrac{-5}{24}.\dfrac{5}{6}+\dfrac{1}{2}\\
=\dfrac{-25}{144}+\dfrac{1}{2}\\
=\dfrac{-25}{144}+\dfrac{72}{144}\\
=\dfrac{47}{144}\\
b) \dfrac{1}{2}+\dfrac{3}{4}-\left ( \dfrac{3}{4}-\dfrac{4}{5} \right )\\
=\dfrac{1}{2}+\dfrac{3}{4}- \dfrac{3}{4}+\dfrac{4}{5} \\
=\dfrac{1}{2}+\dfrac{4}{5} \\
=\dfrac{5}{10}+\dfrac{8}{10} \\
=\dfrac{13}{10}$