Question

\(\left|x-3\right|=9-2x\)

Answer 1

\(\left|x-3\right|=9-2x\)

Th1 \(x-3=-2x+9\)

\(\Leftrightarrow3x-3=9\)

\(\Leftrightarrow3x=9+3\)

\(\Leftrightarrow3x=12\)

\(\Leftrightarrow x=4\)

Th2 : \(x-3=2x-9\) 

\(\Leftrightarrow-x-3=-9\)

\(\Leftrightarrow-x=\left(-9\right)+3\)

\(\Leftrightarrow-x=-6\)

\(\Leftrightarrow x=6\) \(\text{( loại )}\)

Vậy \(x=4\)

 

Answer 2

TH1 : \(\left|x-3\right|=x-3\) khi \(x-3\ge0\Leftrightarrow x\ge3\)

TH2 : \(\left|x-3\right|=-x+3\) khi \(x-3< 0\Leftrightarrow x< 3\)

Ta có : 

\(x-3=9-2x\\ \Leftrightarrow2x+x=9+3\\ \Leftrightarrow3x=12\\ \Leftrightarrow x=4\left(nhận\right)\)

Ta có :

\(-x+3=9-2x\\ \Leftrightarrow-x+2x=9-3\\ \Leftrightarrow x=6\left(loại\right)\)

Vậy S = { 4 }