$\text{Đáp án + Giải thích các bước giải:}$
`|2x+3|=x+2` `(ĐK:x≥-2)`
`=>` \(\left[ \begin{array}{l}2x+3=x+2\\2x+3=-x-2\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}2x-x=2-3\\2x+x=-2-3\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x=-1\\3x=-5\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x=-1(TM)\\x=-\dfrac{5}{3}(TM)\end{array} \right.\)
`\text{Vậy}` `x∈{-1;-(5)/(3)}`
`-----------`
`A=|x-2006|+|2007-x|≥|x-2006+2007-x|=|1|=1`
Dấu '' = '' xảy ra khi :
`(x-2006)(2007-x)≥0`
`+)TH1:`
$\left\{\begin{matrix}x-2006≥0& \\2007-x≥0& \end{matrix}\right.$
`=>` $\left\{\begin{matrix}x≥2006& \\x≤2007& \end{matrix}\right.$
`=>2006≤x≤2007`
`+)TH2:`
$\left\{\begin{matrix}x-2006≤0& \\2007-x≤0& \end{matrix}\right.$
`=>` $\left\{\begin{matrix}x≤2006& \\x≥2007& \end{matrix}\right.$
`=>2007≤x≤2006` ( Loại )
Vậy `GTNNNN` của `A = 1` khi `2006≤x≤2007`
