Answer
$x = 1.50~m$
Work Step by Step
To find the maximum value of $x$, we can assume that the tension in the wire is $T = 500~N$
To find the maximum value of $x$, we can consider the torque about the rotation axis at the hinge:
$\sum \tau_i = 0$
$L~T~sin~150^{\circ}-(1.50~m)(200~N)-x~(300~N) = 0$
$x~(300~N) = L~T~sin~150^{\circ}-(1.50~m)(200~N)$
$x = \frac{(3.00~m)~(500~N)~sin~150^{\circ}-(1.50~m)(200~N)}{300~N}$
$x = 1.50~m$
