Tìm x a) ( 2x/3 – 3 ) : ( -10 ) = 2/5 b) ( x – 1 ) x ( x + 2 )< 0 c) ( x + 3/5 ) x ( x+ 1 )<0 d) ( x - 1/3 ) x ( x + 2/5 )>0

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1. 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:

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

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