Question

Tìm x để :

a ) ( x - \(\frac{1}{3}\) ) ( 5x + 2 ) > 0

b ) ( 5x + 3 ) ( 3x - 2 ) < 0

Answer 1

a) \(\left(x-\frac{1}{3}\right)\left(5x+2\right)>0\)

<=> \(\left[\begin{array}{nghiempt}x-\frac{1}{3}>0\\5x+3< 0\end{array}\right.\) hoặc \(\left[\begin{array}{nghiempt}x-\frac{1}{3}< 0\\5x+3>0\end{array}\right.\)

<=> \(\left[\begin{array}{nghiempt}x>\frac{1}{3}\\5x< 3\end{array}\right.\) hoặc \(\left[\begin{array}{nghiempt}x< \frac{1}{3}\\5x>3\end{array}\right.\)

<=> \(\left[\begin{array}{nghiempt}x>\frac{1}{3}\\x< \frac{3}{5}\end{array}\right.\) hoặc \(\left[\begin{array}{nghiempt}x< \frac{1}{3}\\x>\frac{3}{5}\end{array}\right.\)

Vậy...

Answer 2

a) \(\left(x-\frac{1}{3}\right)\left(5x+2\right)>0\)

\(\Leftrightarrow\begin{cases}x-\frac{1}{3}>0\\5x+2>0\end{cases}\) hoặc \(\begin{cases}x-\frac{1}{3}< 0\\5x+2< 0\end{cases}\)

\(\Leftrightarrow\begin{cases}x>\frac{1}{3}\\x>-\frac{2}{5}\end{cases}\) hoặc \(\begin{cases}x< \frac{1}{3}\\x< -\frac{2}{5}\end{cases}\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x>\frac{1}{3}\\x< -\frac{2}{5}\end{array}\right.\)

b) \(\left(5x+3\right)\left(3x-2\right)< 0\)

\(\Leftrightarrow\begin{cases}5x+3>0\\3x-2< 0\end{cases}\) hoặc \(\begin{cases}5x+3< 0\\3x-2>0\end{cases}\)

\(\Leftrightarrow\begin{cases}x>-\frac{3}{5}\\x< \frac{2}{3}\end{cases}\) hoặc \(\begin{cases}x< -\frac{3}{5}\\x>\frac{2}{5}\end{cases}\) (loại)

\(\Leftrightarrow-\frac{3}{5}< x< \frac{2}{3}\)