Đáp án:
$a)
x=\dfrac{21}{2}\\
b)
-2<x<1\\
c)
-1<x<\dfrac{-3}{5}\\
d)
{\left[\begin{aligned} x>\dfrac{1}{3}\\x<-\dfrac{2}{5}\end{aligned}\right.}\\$
Giải thích các bước giải:
$a)
\left ( \dfrac{2x}{3}-3 \right ):(-10)=\dfrac{2}{5}\\
\Leftrightarrow \dfrac{2x}{3}-3=\dfrac{2}{5}.10\\
\Leftrightarrow \dfrac{2x}{3}-3=4\\
\Leftrightarrow \dfrac{2}{3}x=4+3=7\\
\Leftrightarrow x=\dfrac{3}{2}.7=\dfrac{21}{2}\\
b)
(x-1).(x+2)<0\\
\Leftrightarrow {\left[\begin{aligned}{\left\{\begin{aligned}x-1>0\\x+2<0\end{aligned}\right.}\\{\left\{\begin{aligned}x-1<0\\x+2>0\end{aligned}\right.}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}{\left\{\begin{aligned}x>1\\x<-2\end{aligned}\right.} (loại) \\{\left\{\begin{aligned}x<1\\x>-2\end{aligned}\right.}\end{aligned}\right.}\\
\Leftrightarrow -2<x<1\\
c)
\left ( x+\dfrac{3}{5} \right ).(x+1)<0\\
\Leftrightarrow {\left[\begin{aligned}{\left\{\begin{aligned} x+\dfrac{3}{5}>0\\x+1<0\end{aligned}\right.}\\{\left\{\begin{aligned}x+\dfrac{3}{5}<0\\x+1>0\end{aligned}\right.}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}{\left\{\begin{aligned} x>-\dfrac{3}{5}\\x<-1\end{aligned}\right.} (loại) \\{\left\{\begin{aligned}x<-\dfrac{3}{5}\\x>-1\end{aligned}\right.}\end{aligned}\right.}\\
\Leftrightarrow -1<x<\dfrac{-3}{5}\\
d)
\left ( x-\dfrac{1}{3} \right ).\left ( x+\dfrac{2}{5} \right )>0\\
\Leftrightarrow {\left[\begin{aligned}{\left\{\begin{aligned} x-\dfrac{1}{3}>0\\x+\dfrac{2}{5}>0\end{aligned}\right.}\\{\left\{\begin{aligned}x-\dfrac{1}{3}<0\\x+\dfrac{2}{5}<0\end{aligned}\right.}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}{\left\{\begin{aligned} x>\dfrac{1}{3}\\x>-\dfrac{2}{5}\end{aligned}\right.}\\{\left\{\begin{aligned}x<\dfrac{1}{3}\\x<-\dfrac{2}{5}\end{aligned}\right.}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned} x>\dfrac{1}{3}\\x<-\dfrac{2}{5}\end{aligned}\right.}\\$
