Question

giải phương trình |x-7|-2x=4

Answer 1

Lời giải:

\(|x-7|-2x=4\)

\(\Leftrightarrow |x-7|=2x+4\)

\(\Rightarrow \left\{\begin{matrix} 2x+4\geq 0\\ (x-7)^2=(2x+4)^2\end{matrix}\right.\)

\(\Leftrightarrow \left\{\begin{matrix} x\geq -2\\ 3x^2+30x-33=0\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x\geq -2\\ x^2+10x-11=0\end{matrix}\right.\)

\(\Leftrightarrow \left\{\begin{matrix} x\geq -2\\ (x-1)(x+11)=0\end{matrix}\right.\Rightarrow x=1\)

Answer 2

/x-7/=4+2x

th1 : \(x-7\ge0=>x\ge7\)

=> x-7=4+2x

=>-x=11

=>x=-11(loại)

th2: \(x-7< 0=>x< 7\)

=>7-x=4+2x

=>-3x=-3

=>x=1(tm)

vậy S=\(\left\{1\right\}\)