1. **State the problem:** Solve the inequality $$2(\sqrt{x} + 7) < -18$$. 2. **Understand the problem:** The expression involves a square root, which means the domain of $x$ must satisfy $x \geq 0$ because the square root of a negative number is not a real number. 3. **Analyze the inequality:** Since $\sqrt{x} \geq 0$ for $x \geq 0$, the smallest value of $\sqrt{x} + 7$ is when $x=0$, which gives $\sqrt{0} + 7 = 7$. 4. **Evaluate the left side minimum:** Multiply by 2: $$2 \times 7 = 14$$. 5. **Compare with the right side:** The inequality requires $$2(\sqrt{x} + 7) < -18$$, but the left side is always at least 14, which is greater than -18. 6. **Conclusion:** There is no real $x$ that satisfies the inequality because the left side cannot be less than -18. **Final answer:** No solution.