Đáp án:
$\begin{array}{l}
1)a)\dfrac{4}{9}:\left( {\dfrac{{ - 1}}{7}} \right) + 6\dfrac{5}{9}.\left( {\dfrac{2}{3}} \right)\\
= \dfrac{4}{9}.\left( { - 7} \right) + \dfrac{{59}}{9}.\dfrac{2}{3}\\
= \dfrac{2}{3}.\dfrac{2}{3}.\left( { - 7} \right) + \dfrac{2}{3}.\dfrac{{59}}{9}\\
= \dfrac{2}{3}.\left( { - \dfrac{{14}}{3} + \dfrac{{59}}{9}} \right)\\
= \dfrac{2}{3}.\dfrac{{ - 14.3 + 59}}{9}\\
= \dfrac{2}{3}.\dfrac{{17}}{9}\\
= \dfrac{{34}}{{27}}\\
b){\left( {\dfrac{{ - 1}}{3}} \right)^2}.\dfrac{4}{{11}} + \dfrac{7}{{11}}.{\left( { - \dfrac{1}{3}} \right)^2}\\
= \dfrac{1}{9}.\dfrac{4}{{11}} + \dfrac{7}{{11}}.\dfrac{1}{9}\\
= \dfrac{1}{9}\left( {\dfrac{4}{{11}} + \dfrac{7}{{11}}} \right)\\
= \dfrac{1}{9}.1\\
= \dfrac{1}{9}\\
B2)\\
a)\dfrac{1}{5} + \dfrac{4}{5}.x = - 3\\
\Rightarrow \dfrac{4}{5}.x = - 3 - \dfrac{1}{5}\\
\Rightarrow \dfrac{4}{5}.x = - \dfrac{{16}}{5}\\
\Rightarrow x = - 4\\
Vậy\,x = - 4\\
b)\left| {x + \dfrac{1}{2}} \right| - \dfrac{2}{3} = \sqrt {\dfrac{{16}}{9}} \\
\Rightarrow \left| {x + \dfrac{1}{2}} \right| = \dfrac{4}{3} + \dfrac{2}{3}\\
\Rightarrow \left| {x + \dfrac{1}{2}} \right| = 2\\
\Rightarrow \left[ \begin{array}{l}
x + \dfrac{1}{2} = 2\\
x + \dfrac{1}{2} = - 2
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 2 - \dfrac{1}{2} = \dfrac{3}{2}\\
x = - 2 - \dfrac{1}{2} = - \dfrac{5}{2}
\end{array} \right.\\
Vậy\,x = \dfrac{3}{2};x = - \dfrac{5}{2}\\
B3)\dfrac{x}{{12}} = \dfrac{y}{3} = \dfrac{{x - y}}{{12 - 3}} = \dfrac{{36}}{9} = 4\\
\Rightarrow \left\{ \begin{array}{l}
x = 4.12 = 48\\
y = 4.3 = 12
\end{array} \right.\\
Vậy\,x = 48;y = 12\\
b)\left\{ \begin{array}{l}
\dfrac{x}{2} = \dfrac{y}{3} \Rightarrow y = \dfrac{3}{2}.x\\
\dfrac{y}{5} = \dfrac{z}{4} \Rightarrow y = \dfrac{5}{4}.z
\end{array} \right.\\
\Rightarrow \dfrac{3}{2}.x = y = \dfrac{5}{4}.z\\
\Rightarrow \dfrac{{3x}}{{2.15}} = \dfrac{y}{{15}} = \dfrac{{5z}}{{4.15}}\\
\Rightarrow \dfrac{x}{{10}} = \dfrac{y}{{15}} = \dfrac{z}{{12}} = \dfrac{{x - y + z}}{{10 - 15 + 12}}\\
= \dfrac{{ - 49}}{7} = - 7\\
\Rightarrow \left\{ \begin{array}{l}
x = - 70\\
y = - 105\\
z = - 84
\end{array} \right.\\
Vậy\,x = - 70;y = - 105;z = - 84
\end{array}$
