Áp dụng : $|a| + |b|$ $≥$ $0$ khi $a.b≥0$
$⇒$ $|9x-2020|+|2020-9x| ≥ |9x-2020+2020-9x| = 0$
Dấu " $=$ " khi : `(9x-2020).(2020-9x) ≥ 0`
$TH1$. $\left\{\begin{matrix}9x - 2020 ≥ 0 & \\ 2020-9x≥0 & \\\end{matrix}\right.$ $⇒$ $x= \dfrac{2020}{9}$
$TH2$. $\left\{\begin{matrix}9x - 2020 < 0 & \\ 2020-9x<0 & \\\end{matrix}\right.$ $⇒$ ($KTM$)
Vậy $A_{min}=0$ khi $x=\dfrac{2020}{9}$