Question

|3x-|2x-1||=|x+2|
module.

Answer 1

|3x-|2x-1||=|x+2|

3x - |2x-1| = x+2 =) x ∈ Q
3x - |2x-1| = - (x+2 ) =) 
3x - |2x-1| = -x-2
3x - |2x-1| +x = -2
4x - |2x-1| =-2 =) x = -1/6 

Answer 2

$\Big|3x-|2x-1|\Big|=|x+2| \\ \\ \bullet 3x-|2x-1| = x+2 \Rightarrow |2x-1| = 2x-2 \\ ~~~~~~~ \bullet 2x-1 = 2x-2 \Rightarrow x \in \emptyset \\ ~~~~~~~ \bullet 2x-1 = -2x +2 \Rightarrow 4x = 3 \Rightarrow x = \dfrac{3}{4} \quad \boxed{1} \\ \\ \bullet 3x-|2x-1| = -x-2 \Rightarrow |2x-1| = 4x+2 \\ ~~~~~~~~ \bullet 2x-1 = 4x+2 \Rightarrow 2x = -3 \Rightarrow x = -\dfrac{3}{2} \quad \boxed{2} \\ ~~~~~~~~\bullet 2x-1 = -4x-2 \Rightarrow 6x = -1 \Rightarrow x = -\dfrac{1}{6}\quad \boxed{3}$

$\text{Doar }\boxed{3} verifica \Rightarrow S = \Big\{-\dfrac{1}{6}\Big\}$