Đáp án:

 $2)
a) x=\dfrac{-131}{130}\\
b) x=\dfrac{7}{2}\\
c)
x=\dfrac{17}{6}\\
d)
x=\dfrac{-13}{12}\\
e)
x=-8\\
f)  x=\dfrac{25}{8}\\
5)
a)
A=4950$
b)
$B=\dfrac{99}{100}$

Giải thích các bước giải:

 $2)
a) x+\dfrac{30}{100}x=-1,31\\
\Leftrightarrow x+\dfrac{3}{10}x=\dfrac{-131}{100}\\
\Leftrightarrow \dfrac{10}{10}x+\dfrac{3}{10}x=\dfrac{-131}{100}\\
\Leftrightarrow \dfrac{13}{10}x=\dfrac{-131}{100}\\
\Leftrightarrow x=\dfrac{-131}{100}.\dfrac{10}{13}=\dfrac{-131}{130}\\
b)\left ( x-\dfrac{1}{2} \right ):\dfrac{1}{3}+\dfrac{5}{7}=9\dfrac{5}{7}\\
\Leftrightarrow \left ( x-\dfrac{1}{2} \right ).3=\dfrac{68}{7}-\dfrac{5}{7}\\
\Leftrightarrow \left ( x-\dfrac{1}{2} \right ).3=\dfrac{63}{7}=9\\
\Leftrightarrow x-\dfrac{1}{2}=3\\
\Leftrightarrow x=3+\dfrac{1}{2}\\
\Leftrightarrow x=\dfrac{6}{2}+\dfrac{1}{2}\\
\Leftrightarrow x=\dfrac{7}{2}\\
c)
\dfrac{1}{2}x-\dfrac{3}{4}=\dfrac{14}{9}.\dfrac{3}{7}\\
\Leftrightarrow \dfrac{1}{2}x-\dfrac{3}{4}=\dfrac{2}{3}\\
\Leftrightarrow \dfrac{1}{2}x=\dfrac{2}{3}+\dfrac{3}{4}\\
\Leftrightarrow \dfrac{1}{2}x=\dfrac{8}{12}+\dfrac{9}{12}\\
\Leftrightarrow \dfrac{1}{2}x=\dfrac{17}{12}\\
\Leftrightarrow x=\dfrac{17}{12}.2=\dfrac{17}{6}\\
d)
-\dfrac{5}{6}-x=\dfrac{7}{12}+\dfrac{-1}{3}\\
\Leftrightarrow x=\dfrac{-5}{6}-\dfrac{7}{12}+\dfrac{1}{3}\\
\Leftrightarrow x=\dfrac{-10}{12}-\dfrac{7}{12}+\dfrac{4}{12}\\
\Leftrightarrow x=\dfrac{-13}{12}\\
e)
\dfrac{x+3}{-15}=\dfrac{1}{3}\\
\Leftrightarrow x+3=\dfrac{-15}{3}=-5\\
\Leftrightarrow x=-8\\
f) (4,5-2x).\left ( -1\dfrac{4}{7} \right )=\dfrac{11}{4}\\
\Leftrightarrow (4,5-2x).\dfrac{-11}{7} =\dfrac{11}{4}\\
\Leftrightarrow \dfrac{45}{10}-2x=\dfrac{11}{4}.\dfrac{-7}{11}=\dfrac{-7}{4}\\
\Leftrightarrow 2x=\dfrac{9}{2}+\dfrac{7}{4}\\
\Leftrightarrow 2x=\dfrac{18}{4}+\dfrac{7}{4}\\
\Leftrightarrow 2x=\dfrac{25}{4}\\
\Leftrightarrow x=\dfrac{25}{8}$
5)
a)
Ta có công thức cộng các số tự nhiên liên tiếp nhau là $\dfrac{n(n+1)}{2}$ 
$A=1+2+3+4+...+99+100=\dfrac{100(100+1)}{2}=4950$
b)
$B=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{9900}\\
=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{100}\\
=1-\dfrac{1}{100}\\
=\dfrac{100}{100}-\dfrac{1}{100}\\
=\dfrac{99}{100}$