1. **State the problem:** Solve for $x$ in the equation $$1.6(-2x + 7.3) + 3x = 3.2 - x.$$\n\n2. **Distribute the 1.6:** Multiply $1.6$ by each term inside the parentheses:\n$$1.6 \times -2x = -3.2x,$$\n$$1.6 \times 7.3 = 11.68.$$\nSo the equation becomes:\n$$-3.2x + 11.68 + 3x = 3.2 - x.$$\n\n3. **Combine like terms on the left side:**\n$$(-3.2x + 3x) + 11.68 = 3.2 - x,$$\nwhich simplifies to\n$$0.8x + 11.68 = 3.2 - x.$$\n\n4. **Add $x$ to both sides to get all $x$ terms on one side:**\n$$0.8x + x + 11.68 = 3.2 - \cancel{x} + x,$$\nwhich simplifies to\n$$1.8x + 11.68 = 3.2.$$\n\n5. **Subtract 11.68 from both sides to isolate the $x$ term:**\n$$1.8x + 11.68 - 11.68 = 3.2 - 11.68,$$\nwhich simplifies to\n$$1.8x = -8.48.$$\n\n6. **Divide both sides by 1.8 to solve for $x$:**\n$$x = \frac{-8.48}{1.8}.$$\nShow cancellation:\n$$x = \frac{-\cancel{8.48}}{\cancel{1.8}} \times \frac{1}{1}$$ (simplify numerator and denominator by dividing numerator and denominator by 0.2)\nActually, to simplify, divide numerator and denominator by 0.2:\n$$x = \frac{-8.48 \div 0.2}{1.8 \div 0.2} = \frac{-42.4}{9}.$$\n\n7. **Calculate the decimal value:**\n$$x \approx -4.7111.$$\n\n**Final answer:**\n$$\boxed{x \approx -4.71}.$$