1, $2(x-4)+1=3(x+1)-6$

$⇔2x-8+1=3x+3-6$

$⇔2x-7=3x-3$

$⇔2x-3x=-3+7$

$⇔-x=4$

$⇔x=-4$

Vậy $S=${$-4$}

2, $(x-2)(2x+3)=0$

$⇔$\(\left[ \begin{array}{l}x-2=0\\2x+3=0\end{array} \right.\)

$⇔$\(\left[ \begin{array}{l}x=2\\x=-3/2\end{array} \right.\)

Vậy $S=${$2;-3/2$}

3, $\frac{3x-2}{x+1}=2$ (1) $ĐKXĐ:x$$\neq-1$

Khi đó: (1)$⇒2(x+1)=3x-2$

$⇔2x+2=3x-2$

$⇔2x-3x=-2-2$

$⇔-x=-4$

$⇔x=4(t/m)$

Vậy $S=${$4$} 

`2(x-4)+1=3(x+1)-6`

⇔\(\left[ \begin{array}{l}2x−7=3x+3−6 \\2x−7=3x−3 \end{array} \right.\)

⇔\(\left[ \begin{array}{l}7=3x−3−2x \\7+3=x \end{array} \right.\)

⇔\(\left[ \begin{array}{l}10=x\\x=10\end{array} \right.\)

`(x-2)(2x+3)=0`

⇔\(\left[ \begin{array}{l}x-2=0\\x=2\end{array} \right.\)

⇔\(\left[ \begin{array}{l}2x+3=0\\x=-2/3\end{array} \right.\)

`3x−2=2(x+1)`
`3x-2=2x+2`
`3x=2x+4`
`3x-2x=4`
`x=4`