Question

|x-2|+3=2x

 

Answer 1

\(\left|x-2\right|+3=2x\)

\(\Leftrightarrow\left|x-2\right|=2x-3\)

TH1: x ≥ 2

\(x-2=2x-3\)

\(\Leftrightarrow x=1\left(ktm\right)\)

TH2: x < 2

\(x-2=-2x+3\)

\(\Leftrightarrow x=\dfrac{5}{3}\left(tm\right)\)

Vậy...

Answer 2

Ta có : /x-2/+3=2x ⇒2x-/x-2/=3

nếu x-2 ≥0 ⇒x≥2 ⇒/x-2/=x-2

suy ra 2x-(x-2)=3⇒x=1( ko thoả mãn đk x≥2)

nếu x-2<0⇒x<2⇒/x-2/= - x+2

suy ra 2x-(-x+2)=3⇒x=\(\dfrac{5}{3}\)(tm đk x<2)

Vậy x=\(\dfrac{5}{3}\)