Question

| x + 1 | + | x + 2 | + | x + 3 | = x

Answer 1

\(\left\{{}\begin{matrix}\left|x+1\right|\ge0\forall x\\\left|x+2\right|\ge0\forall x\\\left|x+3\right|\ge0\forall x\end{matrix}\right.\)\(\Rightarrow\left|x+1\right|+\left|x+2\right|+\left|x+3\right|\ge0\forall x\)

=> \(x\ge0\)

Khi đó \(\left|x+1\right|+\left|x+2\right|+\left|x+3\right|=x+1+x+2+x+3\)

= 3x + 6 > x \(\forall x\ge0\)

Do đó phương trình vô nghiệm.

Answer 2

NX: VT ≥ 0 => VP = x ≥ 0

pt <=> 3x + 6 = x

<=> x = -3