`***`Lời giải`***`
1)
`(3x-1)(x-1)<0`
`<=>`\(\left[ \begin{array}{l}\begin{cases} 3x-1<0\\x-1>0 \end{cases}\\\begin{cases} 3x-1>0\\x-1<0 \end{cases}\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}\begin{cases} 3x<1\\x>1 \end{cases}\\\begin{cases} 3x>1\\x<1 \end{cases}\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}\begin{cases} x<\dfrac{1}{3}\\x>1 \end{cases}\\\begin{cases} x>\dfrac{1}{3}\\x<1 \end{cases}\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}\begin{cases} x<\dfrac{1}{3}\\x>1 \end{cases}(L)\\\begin{cases} x>\dfrac{1}{3}\\x<1 \end{cases}(N)\end{array} \right.\)
Vậy `1/3<x<1`
2)
`(-2x+1)(-3x-2)<0`
`<=>-(-2x+1)(3x+2)<0`
`<=>(-2x+1)(3x+2)>0`
`<=>`\(\left[ \begin{array}{l}\begin{cases} -2x+1>0\\3x+2>0 \end{cases}\\\begin{cases}-2x+1<0 \\3x+2<0\end{cases}\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}\begin{cases} -2x>-1\\3x>-2 \end{cases}\\\begin{cases}-2x<-1 \\3x<-2\end{cases}\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}\begin{cases} 2x<1\\x> \dfrac{-2}{3}\end{cases}\\\begin{cases}2x>1 \\x<\dfrac{-2}{3}\end{cases}\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}\begin{cases} x<\dfrac{1}{2}\\x> \dfrac{-2}{3}\end{cases}(N)\\\begin{cases}x>\dfrac{1}{2} \\x<\dfrac{-2}{3}\end{cases}(L)\end{array} \right.\)
Vậy `\frac{-2}{3}<x<\frac{1}{2}`
3)
`(1+4x)(-3x+2)<0`
`<=>`\(\left[ \begin{array}{l}\begin{cases}1+4x>0\\ -3x+2<0\end{cases}\\\begin{cases}1+4x <0\\-3x+2>0\end{cases}\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}\begin{cases}4x>-1\\ -3x<-2\end{cases}\\\begin{cases}4x <-1\\-3x>-2\end{cases}\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}\begin{cases}x>\dfrac{-1}{4} \\ x>\dfrac{2}{3}\end{cases}\\\begin{cases}x <\dfrac{-1}{4} \\x<\dfrac{2}{3}\end{cases}\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l} x>\dfrac{2}{3}\\x <\dfrac{-1}{4} \end{array} \right.\)
Vậy `x>\frac{2}{3}` hoặc `x <\frac{-1}{4}`
