1. **State the problem:** Find the value of $x$ that satisfies the equation $$3(x - 6) - 8x = -2 + 5(2x + 1).$$ 2. **Expand both sides:** $$3x - 18 - 8x = -2 + 10x + 5$$ 3. **Simplify both sides:** $$3x - 8x - 18 = -2 + 10x + 5$$ $$-5x - 18 = 10x + 3$$ 4. **Bring all $x$ terms to one side and constants to the other:** $$-5x - 10x = 3 + 18$$ $$-15x = 21$$ 5. **Divide both sides by $-15$ to solve for $x$:** $$x = \frac{21}{-15}$$ $$x = \frac{\cancel{21}}{\cancel{-15}} \times \frac{1}{1} = -\frac{7}{5}$$ 6. **Convert to decimal:** $$x = -1.4$$ **Final answer:** $x = -1.4$