Question

Tìm x biết:

| 2x - 1| = x +4

HELP ME!

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:

\(1-2x=x+4\)

\(\Rightarrow-x=-3\)

\(\Rightarrow x=3\) ( loại )

Vậy x = 5

Answer 2

Đk: \(x+4\ge0\Rightarrow x\ge-4\)

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

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

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

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

Vậy x=5

Answer 3

Vì \(\left|2x-1\right|\ge0\) Để \(\left|2x-1\right|=x+4\) => \(x+4\ge0\Rightarrow x\ge-4\)

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

TH1 : 2x - 1 = x + 4 <=> 2x - x = 4 + 1 => x = 5 (TM)

TH2 : 2x - 1 = - x - 4 <=> 2x + x = - 4 + 1 <=> 3x = - 3 => x = - 1(TM)

Vậy x = { - 1; 5 }