1. **State the problem:** Solve the inequality $$\frac{1}{8} - 2x - 6 > \frac{1}{32} - x + 11$$. 2. **Rewrite the inequality:** Combine like terms and isolate variable terms on one side. 3. **Subtract $$\frac{1}{32}$$ from both sides:** $$\frac{1}{8} - 2x - 6 - \frac{1}{32} > -x + 11$$ 4. **Simplify constants on the left:** Find common denominator for $$\frac{1}{8}$$ and $$\frac{1}{32}$$ which is 32. $$\frac{4}{32} - \frac{1}{32} = \frac{3}{32}$$ So, $$\frac{3}{32} - 2x - 6 > -x + 11$$ 5. **Combine $$\frac{3}{32}$$ and $$-6$$:** Convert 6 to $$\frac{192}{32}$$ $$\frac{3}{32} - \frac{192}{32} = -\frac{189}{32}$$ So, $$-\frac{189}{32} - 2x > -x + 11$$ 6. **Add $$2x$$ to both sides:** $$-\frac{189}{32} > -x + 11 + 2x$$ $$-\frac{189}{32} > x + 11$$ 7. **Subtract 11 from both sides:** $$-\frac{189}{32} - 11 > x$$ Convert 11 to $$\frac{352}{32}$$ $$-\frac{189}{32} - \frac{352}{32} = -\frac{541}{32}$$ 8. **Final inequality:** $$x < -\frac{541}{32}$$ **Answer:** $$x < -\frac{541}{32}$$