1. **State the problem:** Solve the inequality $$\log_{0.5}(x - 3) < 1$$ and determine which interval satisfies this inequality from the given options. 2. **Analyze the domain:** Since the logarithm $$\log_{0.5}(x - 3)$$ is defined only if its argument is positive: $$x - 3 > 0 \implies x > 3$$ 3. **Rewrite the inequality using exponential form:** The inequality $$\log_{0.5}(x - 3) < 1$$ means: $$(x - 3) < (0.5)^1$$ Because the base $$0.5$$ is between 0 and 1, the logarithm is a decreasing function, so the inequality direction reverses when converting from log to exponential: $$\log_{0.5}(a) < b \iff a > (0.5)^b$$ Therefore we have: $$x - 3 > 0.5$$ 4. **Solve the inequality:** $$x - 3 > 0.5 \implies x > 3.5$$ 5. **Combine with domain restriction:** The domain requires $$x > 3$$ and the inequality requires $$x > 3.5$$. Hence, overall: $$x > 3.5$$ 6. **Evaluate the interval options:** - $$(3.5; +\infty)$$ satisfies $$x > 3.5$$. - Other intervals do not satisfy this combined condition. \textbf{Final answer:} $$(3.5; +\infty)$$