\(\left|x+1\right|-\left|-2x-2\right|=2\)
\(\Leftrightarrow\left|x+1\right|-\left|-2\left(x+1\right)\right|=2\)
\(\Leftrightarrow\left|x+1\right|-2\left|x+1\right|=2\)
\(\Leftrightarrow-\left|x+1\right|=2\)
\(\Leftrightarrow\left|x+1\right|=-2\)
\(\Leftrightarrow\left|x+1\right|+2=0\)
Mà: \(\left|x+1\right|\ge0\forall x\Rightarrow\left|x+1\right|+2\ge2>0\)
\(\Leftrightarrow\left|x+1\right|+2=0\) (vô lí)
Vậy phương trình vô nghiệm:
\(x\in\varnothing\)
=>|x+1|-2|x+1|=2
=>-|x+1|=2
=>|x+1|=-2(vô lý)
Vậy: \(x\in\varnothing\)
\(TH_1:\left\{{}\begin{matrix}x+1\ge0\\-2x-2\ge0\end{matrix}\right.\)
\(\left(1\right)\left(x+1\right)-\left(-2x-2\right)=2\)
\(\Leftrightarrow x+1+2x+2=2\)
\(\Leftrightarrow3x+3=2\)
\(\Leftrightarrow x=-\dfrac{1}{3}\left(l\right)\)
\(TH_2:\left\{{}\begin{matrix}x+1< 0\\-2x-2< 0\end{matrix}\right.\)
\(\left(1\right)\left(x+1\right)-\left(-\left(-2x-2\right)\right)=2\)
\(\Leftrightarrow-x-1+2x+2=2\)
\(\Leftrightarrow x+1=2\)
\(\Leftrightarrow x=1\left(l\right)\)
Vậy tập nghiệm rỗng.
|x+1|−|−2x−2|=2|x+1|−|−2x−2|=2
⇔|x+1|−|−2(x+1)|=2⇔|x+1|−|−2(x+1)|=2
⇔|x+1|−2|x+1|=2⇔|x+1|−2|x+1|=2
⇔−|x+1|=2⇔−|x+1|=2
⇔|x+1|=−2⇔|x+1|=−2
⇔|x+1|+2=0⇔|x+1|+2=0
Mà: |x+1|≥0∀x⇒|x+1|+2≥2>0|x+1|≥0∀x⇒|x+1|+2≥2>0
⇔|x+1|+2=0⇔|x+1|+2=0 (loại)
Vậy phương trình vô nghiệm:
x∈∅
