Question

Tìm x biết:

|x − 5| + |2x − 1| = 2x + 3.

Answer 1

TH1: \(x\ge5\)

<=> \(\left\{{}\begin{matrix}\left|x-5\right|=x-5\\\left|2x-1\right|=2x-1\end{matrix}\right.\)

PT <=> \(x-5+2x-1=2x+3\)

<=> x = 9 (Tm)

TH2: \(\dfrac{1}{2}\le x< 5\)

<=> \(\left\{{}\begin{matrix}\left|x-5\right|=5-x\\\left|2x-1\right|=2x-1\end{matrix}\right.\)

PT <=> 5 - x + 2x -1 = 2x + 3

<=> x = 1(Tm)

TH3: \(x< \dfrac{1}{2}\)

<=> \(\left\{{}\begin{matrix}\left|x-5\right|=5-x\\\left|2x-1\right|=1-2x\end{matrix}\right.\)

PT <=> \(5-x+1-2x=2x+3\)

<=> \(5x=3< =>x=\dfrac{3}{5}\left(l\right)\)

KL: x \(\in\left\{1;9\right\}\)