Question

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

Answer 1

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

\(\Leftrightarrow\left[{}\begin{matrix}3x+1=x+1\\3x+1=-x-1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{1}{2}\end{matrix}\right.\)

Vậy Phương Trình có Tập Nghiệm \(S=\left\{0;-\dfrac{1}{2}\right\}\)

Answer 2

Cách khác :
\(\text{|}3x+1\text{|}=\text{|}x+1\text{|}\)

⇔ \(\left(3x+1\right)^2=\left(x+1\right)^2\)

⇔ \(\left(3x+1\right)^2-\left(x+1\right)^2=0\)

\(\text{⇔}\left(3x+1-x-1\right)\left(3x+1+x+1\right)=0\)

\(\text{⇔}2x\left(4x+2\right)=0\)

\(\text{⇔}x=0orx=-\dfrac{1}{2}\)

KL.....