Question

[Vũ Thị Hoa]

/ x + 1 / + / x + 2 / + / x + 3 / = 4x - 4 = 9999

Answer 1

[Lê Tài Bảo Châu]

\(|x+1|+|x+2|+|x+3|=4x-4\left(1\right)\)

Vì \(\hept{\begin{cases}|x+1|\ge0;\forall x\\|x+2|\ge0;\forall x\\|x+3|\ge0;\forall x\end{cases}}\)

\(\Rightarrow|x+1|+|x+2|+|x+3|\ge0;\forall x\)

Mà \(|x+1|+|x+2|+|x+3|=4x-4\)

\(\Rightarrow4x-4\ge0\)

\(\Rightarrow4x\ge4\)

\(\Rightarrow x\ge1>0\)

\(\Rightarrow\hept{\begin{cases}|x+1|=x+1\\|x+2|=x+2\\|x+3|=x+3\end{cases}}\)(2) 

Thay (2) vào (1) ta được :

\(x+1+x+2+x+3=4x-4\)

\(\Leftrightarrow3x+6=4x-4\)

\(\Leftrightarrow3x-4x=-4-6\)

\(\Leftrightarrow-x=-10\)

\(\Leftrightarrow x=10\)

Vậy x=10