Question

Tim x

|2x-1|=x+4

Answer 1

`|2x-1|=x+4`

`@TH1:2x-1 >= 0=>x >= 1/2 =>|2x-1|=2x-1`

   `=>2x-1=x+4`

   `=>x=5` (t/m)

`@TH2:2x-1 < 0=>x < 1/2=>|2x-1|=1-2x`

    `=>1-2x=x+4`

   `=>3x=-3=>x=-1` (t/m)

Vậy `x in {-1;5}`

Answer 2

x= 5 hoặc -1.

Answer 3

`|2x-1|=x+4`

=>\(\left[{}\begin{matrix}2x-1=x+4\\2x-1=-x-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x-1-x-4=0\\2x-1+x+4=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\3x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-1\end{matrix}\right.\)

Answer 4

TH1: x > 1/2

=> |2x - 1| = 2x - 1

<=> 2x - 1 = x + 4

<=> x = 5 (TM)

TH2: x < 1/2

=> |2x - 1| = 1 - 2x

<=> 1 - 2x = x + 4

<=> -3x = 3

<=> x = -1 (TM)

vậy x ∈ {-1; 5}

Answer 5

Vậy $x\in \{-1;5\}$