Question

Tìm x:

a, | x - 3 | = 2x + 4

b, | 2x + 1 | = x - 2

c, | x + 3 | + | x + 2 | = 6

Answer 1

a) \(|x-3|=2x+4\)

\(\Rightarrow\left[{}\begin{matrix}x-3=2x+4\\x-3=-2x-4\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x-2x=4+3\\x+2x=-4+3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}-x=7\\3x=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-7\\x=-\dfrac{1}{3}\end{matrix}\right.\)

b) \(|2x+1|=x-2\)

\(\Rightarrow\left[{}\begin{matrix}2x+1=x-2\\2x+1=-x+2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x-x=-2-1\\2x+x=2-1\end{matrix}\right.\)

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