Question

Tìm x thỏa mãn:

\(\left|x+1\right|+\left|x-2\right|+\left|x+7\right|=5x-10.\)

Answer 1

Cách 2: Do \(\left|x\right|\ge0\forall x\) nên \(\left|x+1\right|+\left|x-2\right|+\left|x+7\right|\ge0\)

\(\Rightarrow5x-10\ge0\Rightarrow x\ge2\)

Với \(x\ge2\), ta có : \(x+7>0;x+1>0;x-2\ge0\)

Suy ra \(x+1+x-2+x+7=5x-10\)

\(\Leftrightarrow-2x=-16\Leftrightarrow x=8\left(tm\right)\)

Vậy x = 8.

Answer 2

Cách 1: Với \(x\le-7\), ta có : \(x+7\le0;x+1< 0;x-2< 0\)

Suy ra \(-x-1-x+2-x-7=5x-10\)

\(\Leftrightarrow-8x=-4\Leftrightarrow x=\frac{1}{2}\left(l\right)\)

Với \(-7< x\le-1\), ta có : \(x+7>0;x+1\le0;x-2< 0\)

Suy ra \(-x-1-x+2+x+7=5x-10\)

\(\Leftrightarrow-6x=-18\Leftrightarrow x=3\left(l\right)\)

Với \(-1< x\le2\), ta có : \(x+7>0;x+1>0;x-2\le0\)

Suy ra \(x+1-x+2+x+7=5x-10\)

\(\Leftrightarrow-6x=-20\Leftrightarrow x=\frac{10}{3}\left(l\right)\)

Với \(x>2\), ta có : \(x+7>0;x+1>0;x-2>0\)

Suy ra \(x+1+x-2+x+7=5x-10\)

\(\Leftrightarrow-2x=-16\Leftrightarrow x=8\left(tm\right)\)

Vậy x = 8.