1. **State the problem:** Solve the inequality $$6(1 + 5x) \geq 246$$ given the condition $$x < -1$$. 2. **Write the formula and rules:** To solve inequalities, we first expand and simplify the expression, then isolate the variable. Remember, when multiplying or dividing by a negative number, the inequality sign reverses. 3. **Expand the left side:** $$6(1 + 5x) = 6 \times 1 + 6 \times 5x = 6 + 30x$$ 4. **Rewrite the inequality:** $$6 + 30x \geq 246$$ 5. **Subtract 6 from both sides:** $$6 + 30x - 6 \geq 246 - 6$$ $$30x \geq 240$$ 6. **Divide both sides by 30:** $$\frac{30x}{30} \geq \frac{240}{30}$$ $$\cancel{30}x \geq \cancel{30}8$$ $$x \geq 8$$ 7. **Combine with the given condition:** We have $$x \geq 8$$ from the inequality and $$x < -1$$ from the condition. 8. **Interpret the solution:** There is no value of $$x$$ that satisfies both $$x \geq 8$$ and $$x < -1$$ simultaneously. **Final answer:** $$\text{No solution}$$ because the two conditions contradict each other.