1/

l2x+3l=x+2(1)

ta co l2x+3l=\(\hept{\begin{cases}2x+3voix\ge\frac{-3}{2}\\-2x-3voix< \frac{-3}{2}\end{cases}}\)

TH1: neu x>= -3/2 thi (1) <=>2x+3=x+2=>x=-1(chon)

TH2: neu x<= -3/2 thi (1) <=> -2x-3=x+2=>-3x=5=>x=-5/3(chon)

 2/

de A dat gtnn thi lx-2006l va l2007l dat gtnn

ma lx-2006l va l2007-xl >=0

=> gtnn cua lx-2006l=0;l2007-xl=0

=> x=2006 hoac 2007

=> gtnn A=1

hihi o may quá

toi cung dang ngum

a) \(\left|2x+3\right|=x+2\)

\(TH1:2x+3=x+2\)

\(\Rightarrow2x-x=2-3\)

\(x=-1\)

\(TH2:2x+3=-\left(x+2\right)\)

\(2x+3=-x-2\)

\(2x+x=-2-3\)

\(3x=-5\)

\(x=\frac{-5}{3}\)

KL: x= -1; x= -5/3

b) bn tham khảo câu này nha

gõ link : http://olm.vn/hoi-dap/question/650540.html

CHÚC BN HỌC TỐT!!!

a, x=-1

b = giá trị nhỏ nhất của a là 1

\(A=\left|x-2006\right|+\left|2007-x\right|\ge\left|x-2006+2007-x\right|=\left|1\right|=1\)

\(minA=1\Leftrightarrow\left(x-2006\right)\left(2007-x\right)\ge0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-2006\ge0\\2007-x\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}x-2006\le0\\2007-x\le0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow2006\le x\le2007\)

\(A=\left|x-2006\right|+\left|2007-x\right|\)

Vì \(x>2007\) nên \(2x-4013>4014-4013=1\)

\(\Rightarrow A>1\)

Vậy \(A_{min}=1\Leftrightarrow2006\le x\le2007\)

Áp dụng bđt \(\left|a\right|+\left|b\right|\ge\left|a+b\right|\)
\(A\ge\left|x-2016+2017-x\right|=1\)
Vậy minA=1

Ta có \(A=\left|x-2006\right|+\left|2007-x\right|\)

\(=\left|2006-x\right|+\left|x-2007\right|\)

Ta có \(A=\left|2006-x\right|+\left|x-2007\right|\ge\left|2006-x+x-2007\right|=1\)

Dấu "=" xảy ra khi và chỉ \(2006\le x\le2007\)

Vậy GTNN A=1 khi \(2006\le x\le2007\)

Ta có :

\(A=\left|x-2006\right|+\left|2007-x\right|\ge\left|x-2006+2007-x\right|\)

\(\Rightarrow A\ge1\)

\(\Rightarrow A_{min}=1\)

\(\Leftrightarrow\left(x-2006\right)\left(2007-x\right)\ge0\)

Ta có bảng xét dấu :

\(\Rightarrow2006\le x\le2007\)

2005<x<2008

Ta có :

A=|x−2006|+|2007−x|≥|x−2006+2007−x|

⇒A≥1

⇒Amin=1

⇔(x−2006)(2007−x)≥0

Ta có bảng xét dấu :

xx-2006( x - 2006 )( 2007 - x )20062007002007-x0__++++00+__

⇒2006≤x≤2007