1. **State the problem:** We have a right triangle with one angle of 30° and the leg opposite this angle labeled as $x - 3$. We need to solve for $x$. 2. **Recall the formula:** In a right triangle, the side opposite a 30° angle is half the length of the hypotenuse. This is a property of 30°-60°-90° triangles. 3. **Set up the equation:** Let the hypotenuse be $h$. Then, $$x - 3 = \frac{h}{2}$$ 4. **Express the hypotenuse in terms of $x$:** The hypotenuse is twice the side opposite 30°, so $$h = 2(x - 3)$$ 5. **Use the Pythagorean theorem:** The other leg (adjacent to 30°) is $\sqrt{3}$ times the side opposite 30°, so $$\text{adjacent leg} = \sqrt{3}(x - 3)$$ 6. **Since the problem only asks to solve for $x$ given the leg opposite 30° is $x - 3$, and no other lengths are given, we assume the triangle is valid for any $x$ such that $x - 3 > 0$. 7. **Solve inequality:** $$x - 3 > 0$$ $$x > 3$$ **Final answer:** $$\boxed{x > 3}$$ This means $x$ must be greater than 3 for the triangle to be valid with the given side length.