Question

Tìm x biết:

|2x-1|-x=4

*Lưu ý: 2x tức là 2 nhân x

Giúp mình nhanh nhé, Cần gấp

Answer 1

\(\left|2x-1\right|-x=4\)

+) Xét \(x\ge\frac{1}{2}\) có:
\(2x-1-x=4\)

\(\Rightarrow x=5\) ( t/m)

+) Xét \(x< \frac{1}{2}\) có:
\(1-2x-x=4\)

\(\Rightarrow-3x=3\)

\(\Rightarrow x=-1\) (t/m)

Vậy \(x\in\left\{5;-1\right\}\)

Answer 2

\(\left|2x-1\right|-x=4\)

\(\Rightarrow\left|2x-1\right|=4+x\)

Đk:\(4+x\ge0\Rightarrow x\ge-4\)

\(\Rightarrow\left[\begin{matrix}2x-1=4+x\\2x-1=-4-x\end{matrix}\right.\)

\(\Rightarrow\left[\begin{matrix}x=5\left(tm\right)\\x=-1\left(tm\right)\end{matrix}\right.\)

Vậy....