tìm giá trị nguyên của x để biểu thức m = 2022x-2020/3x+2 có giá trị nhỉ nhất

$M$ $=$ $\frac{2022x - 2020}{3x + 2}$

$M$ $=$ $\frac{2022x + 1348 - 3368}{3x + 2}$

$M$ $=$ $\frac{674(3x + 2) - 3368}{3x + 2}$

$M$ $=$ $\frac{674(3x + 2)}{3x + 2}$ $-$ $\frac{3368}{3x + 2}$

$M$ $=$ $674$ $-$ $\frac{3368}{3x + 2}$

$⇒$ $M_{min}$ $⇔$ $\frac{3368}{3x + 2}$ $đạt$ $GTLN$

$Nếu$ $3x$ $+$ $2$ $>$ $0$ $thì$ $\frac{3368}{3x + 2}$ $>$ $0$

$Nếu$ $3x$ $+$ $2$ $<$ $0$ $thì$ $\frac{3368}{3x + 2}$ $<$ $0$

$⇒$ $M_{min}$ $⇔$ $3x$ $+$ $2$ $đạt$ $GTNN$ và $3x$ $+$ $2$ $>$ $0$

$Do$ $đó$ $3x$ $+$ $2$ $=$ $1$

$⇒$ $x$ $=$ $\frac{-1}{3}$

$⇒$ $M_{min}$ $=$ $674$ $-$ $\frac{3368}{1}$

        $M_{min}$ $=$ $674$ $-$ $3368$

        $M_{min}$ $=$ $-2694$

$Vậy$ $M_{min}$ $=$ $-2694$ $khi$ $x$ $=$ $\frac{-1}{3}$