To find the values of x that satisfy both inequalities, we can solve each inequality separately and then find the intersection of their solution sets.

1) 3 + 3x > 0
Subtracting 3 from both sides:
3x > -3
Dividing by 3:
x > -1

2) 2 - 3x > 14
Subtracting 2 from both sides:
-3x > 12
Dividing by -3 (note that dividing by a negative number requires flipping the inequality sign):
x < -4

The solution set for the first inequality is x > -1 and for the second inequality is x < -4. To find the intersection of the solution sets, we look for the values of x that satisfy both conditions. So, the values of x that satisfy both inequalities are:
-4 < x < -1