Question

184.

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

b) \(\left|x-1\right|=\left|3x-5\right|\)

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

d) \(\left|3x-5\right|=x-2\)

e) \(\left|3x-1\right|=1-3x\)

Answer 1

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

\(\Leftrightarrow\left[{}\begin{matrix}2x-\left(x+1\right)=2\left(đk:x\ge0;x+1\ge0\right)\\2\cdot\left(-x\right)-\left(x+1\right)=2\left(đk:x< 0;x+1\ge0\right)\\2x-\left(-\left(x+1\right)\right)=2\left(đk:x\ge0;x+1< 0\right)\\2\cdot\left(-x\right)-\left(-\left(x+1\right)\right)=2\left(đk:x< 0:x+1< 0\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\left(đk:x\ge0;x\ge-1\right)\\x=-1\left(đk:x< 0;x\ge-1\right)\\x=\dfrac{1}{3}\left(đk:x\ge0;đk:x< -1\right)\\x=-1\left(đk:x< 0;x< -1\right)\end{matrix}\right.\)

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

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

Vậy tập nghiệm phương trình (1) là \(S=\left\{-1;3\right\}\)

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