#andy

\[\begin{array}{l}
a)\dfrac{1}{4}x + \dfrac{5}{9} = \dfrac{1}{3}\\
 \Leftrightarrow \dfrac{1}{4}x =  - \dfrac{2}{9}\\
 \Leftrightarrow x =  - \dfrac{8}{9}\\
Vậy\,\,x =  - \dfrac{8}{9}\\
b)\dfrac{3}{4} - \left( {x - \dfrac{2}{5}} \right) = \dfrac{{11}}{{12}}\\
 \Leftrightarrow \dfrac{3}{4} - x + \dfrac{2}{5} = \dfrac{{11}}{{12}}\\
 \Leftrightarrow \dfrac{{23}}{{20}} - x = \dfrac{{11}}{{12}}\\
 \Leftrightarrow x = \dfrac{7}{{30}}\\
Vậy\,\,x = \dfrac{7}{{30}}\\
c)\left| {x + \dfrac{1}{3}} \right| + 1 = 4\\
 \Leftrightarrow \left| {x + \dfrac{1}{3}} \right| = 3\\
 \Leftrightarrow \left[ \begin{array}{l}
x + \dfrac{1}{3} = 3\\
x + \dfrac{1}{3} =  - 3
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{8}{3}\\
x =  - \dfrac{{10}}{3}
\end{array} \right.\\
 \Rightarrow S = \left\{ {\dfrac{8}{3}; - \dfrac{{10}}{3}} \right\}\\
d){27^x} = {3^{x + 2}}\\
 \Leftrightarrow {3^{3x}} = {3^{x + 2}}\\
 \Leftrightarrow {3^3}{.3^x} = {3^{x + 2}}\\
 \Leftrightarrow 3x = x + 2\\
 \Leftrightarrow 3x - x = 2\\
 \Leftrightarrow 2x = 2\\
 \Leftrightarrow x = 1\\
Vậy\,\,x = 1
\end{array}\]

Đáp án:

$2)\\ a) x=\dfrac{-8}{9}\\ b) x=\dfrac{7}{30}\\ c) \left[\begin{array}{l} x=\dfrac{8}{3}  \\ x=-\dfrac{10}{3}\end{array} \right.\\ d) x=1.$

Giải thích các bước giải:

$2)\\ a)\dfrac{1}{4}x+\dfrac{5}{9}=\dfrac{1}{3}\\ \Leftrightarrow \dfrac{1}{4}x=\dfrac{1}{3}-\dfrac{5}{9}\\ \Leftrightarrow \dfrac{1}{4}x=\dfrac{3}{9}-\dfrac{5}{9}\\ \Leftrightarrow \dfrac{1}{4}x=\dfrac{-2}{9}\\ \Leftrightarrow x=\dfrac{-2}{9}.4\\ \Leftrightarrow x=\dfrac{-8}{9}\\ b)\dfrac{3}{4}-\left(x-\dfrac{2}{5}\right)=\dfrac{11}{12}\\ \Leftrightarrow \dfrac{3}{4}-x+\dfrac{2}{5}=\dfrac{11}{12}\\ \Leftrightarrow -x=\dfrac{11}{12}-\dfrac{3}{4}-\dfrac{2}{5}\\ \Leftrightarrow -x=\dfrac{11.5}{12.5}-\dfrac{3.15}{4.15}-\dfrac{2.12}{5.12}\\ \Leftrightarrow -x=\dfrac{55}{60}-\dfrac{45}{60}-\dfrac{24}{60}\\ \Leftrightarrow -x=\dfrac{55-45-24}{60}\\ \Leftrightarrow -x=\dfrac{-14}{60}\\ \Leftrightarrow -x=\dfrac{-7}{30}\\ \Leftrightarrow x=\dfrac{7}{30}\\ c)\left|x+\dfrac{1}{3}\right|+1=4\\ \Leftrightarrow \left|x+\dfrac{1}{3}\right|=3\\ \Leftrightarrow \left[\begin{array}{l} x+\dfrac{1}{3} =3 \\ x+\dfrac{1}{3}=-3\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=3-\dfrac{1}{3}  \\ x=-3-\dfrac{1}{3}\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=\dfrac{8}{3}  \\ x=-\dfrac{10}{3}\end{array} \right.\\ d)27^x=3^{x+2}\\ \Leftrightarrow (3^3)^x=3^{x+2}\\ \Leftrightarrow 3^{3x}=3^{x+2}\\ \Leftrightarrow 3x=x+2\\ \Leftrightarrow 2x=2\\ \Leftrightarrow x=1.$