Basic Circuit Analysis with voltage source and current source (KCL)
The first problem I see is here:
$$ -\left( \frac{15+V_x}{3} \right) - \left( \frac{V_x}{2} \right) + 10 = 0$$
If you want \$i_1\$ to be the current out of the x node, then you need first term to be \$-\left(\frac{V_x - 15}{3}\right)\$, not \$-\left( \frac{15+V_x}{3} \right)\$.
Keeping track of the sign conventions you choose is one of the trickiest parts of these problems. It might help if you add current arrows indicating the directions to your schematic.