1. **State the problem:** Solve for $x$ in the equation $$1.6 (-2x + 7.3) + 3x = 3.2 - x.$$\n\n2. **Distribute 1.6 across the parentheses:**\n$$1.6 \times -2x + 1.6 \times 7.3 + 3x = 3.2 - x$$\n$$-3.2x + 11.68 + 3x = 3.2 - x$$\n\n3. **Combine like terms on the left side:**\n$$(-3.2x + 3x) + 11.68 = 3.2 - x$$\n$$0.8x + 11.68 = 3.2 - x$$\n\n4. **Add $x$ to both sides to get all $x$ terms on one side:**\n$$0.8x + x + 11.68 = 3.2 - \cancel{x} + x$$\n$$1.8x + 11.68 = 3.2$$\n\n5. **Subtract 11.68 from both sides to isolate the $x$ term:**\n$$1.8x + \cancel{11.68} - 11.68 = 3.2 - 11.68$$\n$$1.8x = -8.48$$\n\n6. **Divide both sides by 1.8 to solve for $x$:**\n$$x = \frac{-8.48}{1.8}$$\n$$x = -\frac{8.48}{1.8}$$\n\n7. **Simplify the fraction:**\n$$x = -4.7111...$$ (rounded to 4 decimal places)\n\n**Final answer:**\n$$x \approx -4.7111.$$