Third Floor

If the value of $x$ satisfying $\left| 2x-1 \right| =3\lfloor x \rfloor +2\left\{ x \right\}$ is $A$ , find $2016A$ .

Notations :

• $\lfloor \cdot \rfloor$ denotes the floor function .

• $\{ \cdot \}$ denotes the fractional part function .

• $| \cdot |$ denotes the absolute value function.