To solve this inequality, we first need to simplify the expression.

[ {3}^{1 - x} = \frac{3}{3^x} ]

Now our inequality becomes:

[ \frac{3}{3^x} < \sqrt{3} ]

Multiplying both sides by (3^x), we get:

[ 3 < \sqrt{3} \cdot 3^x ]

[ 3 < 3^{1.5} \cdot 3^x ]

[ 3 < 3^{1.5 + x} ]

[ 3 < 3^{x+3/2} ]

Since (3 = 3^1), this inequality simplifies to:

[ 1 < x + \frac{3}{2} ]

[ \frac{1}{2} < x ]

Therefore, the solution to the inequality ( {3}^{1 - x} < \sqrt{3} ) is ( x > \frac{1}{2} ).