Question

[Vũ Kiều Linh]

|x+1|+|x|=3 với x<-1.tìm x

Answer 1

[Phước Lộc]

ta có

\(\left|x+1\right|+\left|x\right|=3\)

vì \(\left|x+1\right|\ge0\)và \(\left|x\right|\ge0\)

nên \(\left|x\right|+\left|x+1\right|=0+3=1+2=2+1=3+0\)

\(\Rightarrow\left|x\right|\in\left\{0;1;2;3\right\}\)

\(\Rightarrow x\in\left\{0;\pm1;\pm2;\pm3\right\}\)

mà \(x< -1\) nên \(x\in\left\{-2;-3\right\}\)