1. **State the problem:** Solve for $x$ in the equation $$3x - 2(8x + 8) = -(7x - 10) - 2x.$$\n\n2. **Apply the distributive property:** Multiply $-2$ by each term inside the parentheses on the left side, and distribute the negative sign on the right side.\n$$3x - 2 \times 8x - 2 \times 8 = -1 \times 7x + 1 \times 10 - 2x$$\nwhich simplifies to\n$$3x - 16x - 16 = -7x + 10 - 2x.$$\n\n3. **Combine like terms on each side:**\nLeft side: $3x - 16x = -13x$, so left side is $$-13x - 16.$$\nRight side: $-7x - 2x = -9x$, so right side is $$-9x + 10.$$\n\n4. **Rewrite the equation:**\n$$-13x - 16 = -9x + 10.$$\n\n5. **Add $13x$ to both sides to get all $x$ terms on the right:**\n$$\cancel{-13x} - 16 + 13x = -9x + 10 + 13x$$\nwhich simplifies to\n$$-16 = 4x + 10.$$\n\n6. **Subtract 10 from both sides to isolate the term with $x$:**\n$$-16 - 10 = 4x + \cancel{10} - 10$$\nwhich simplifies to\n$$-26 = 4x.$$\n\n7. **Divide both sides by 4 to solve for $x$:**\n$$\frac{-26}{\cancel{4}} = \frac{4x}{\cancel{4}}$$\nwhich simplifies to\n$$x = -\frac{26}{4}.$$\n\n8. **Simplify the fraction:**\n$$x = -\frac{13}{2}.$$\n\n**Final answer:** $$x = -\frac{13}{2}.$$