Question

Tìm x, biết :

​/x+1/+/x+4/=3x

Answer 1

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

TH1 : \(x< -4\) ; ta có :

\(-\left(x+1\right)+\left[-\left(x+4\right)\right]=3x\)

\(-2x+5=3x\)

\(-2x-3x=5\)

\(-5x=5\)

\(x=-1\left(KTM\right)\)

TH2 : \(-4\le x< -1\) ; ta có :

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

\(3=3x\)

\(x=1\left(KTM\right)\)

TH3 : \(x\ge-1\) ; ta có : 

\(\left(x+1\right)\left(x+4\right)=3x\)

\(2x+5=3x\)

\(x=5\left(TM\right)\)

Vậy \(x=5\)

Answer 2

Ta có : \(\left|x+1\right|+\left|x+4\right|=3x\)

Vì vế trái luôn dương nên x > 0

Suy ra pt trở thành  \(\left(x+1\right)+\left(x+4\right)=3x\Leftrightarrow x=5\)