3x - 1 - (x + 2) = 2, 3x - 1 >= 0, x + 2 >= 0
-(3x - 1) - (x + 2) = 2, 3x - 1 < 0, x + 2 >= 0
3x - 1 - (- (x + 2)) = 2, 3x - 1 >= 0, x + 2 < 0
-(3x - 1) - (-(x + 2)) = 2, 3x -1 < 0, x + 2 < 0
=> x = \(\dfrac{5}{2}\), x >= \(\dfrac{1}{3}\), x >= -2
=> x = -\(\dfrac{3}{4}\), x < \(\dfrac{1}{3}\), x >= -2
=> x = \(\dfrac{1}{4}\), x >= \(\dfrac{1}{3}\), x < -2
=> x = \(\dfrac{1}{2}\), x < \(\dfrac{1}{3}\), x < -2
=> x = \(\dfrac{5}{2}\)
=> x = \(-\dfrac{3}{4}\)
=> x € tập hợp rỗng
=> x € tập hợp rỗng
Vậy: S = {\(-\dfrac{3}{4}\);\(\dfrac{5}{2}\)}
Có: \(\left\{{}\begin{matrix}\left|3x-1\right|=\left\{{}\begin{matrix}3x-1\forall x\ge\dfrac{1}{3}\\1-3x\forall x< \dfrac{1}{3}\end{matrix}\right.\\\left|x+2\right|=\left\{{}\begin{matrix}x+2\forall x\ge-2\\-x-2\forall x< -2\end{matrix}\right.\end{matrix}\right.\)
Xét: \(x\ge\dfrac{1}{3}.\) Khi đó: \(3x-1-x-2=2\)
\(2x-3=2\)
\(x=\dfrac{5}{2}\left(TM\right)\)
Xét: \(-2\le x< \dfrac{1}{3}.\) Khi đó: \(1-3x-x-2=2\)
\(-1-4x=2\)
\(1+4x=-2\)
\(x=-\dfrac{3}{4}\left(TM\right)\)
Xét: \(x< -2.\) Khi đó: \(1-3x+x+2=2\)
\(3-2x=2\)
\(x=\dfrac{1}{2}\left(loai\right)\)
Vậy \(x=\dfrac{5}{2}orx=-\dfrac{3}{4}\)
