Solve for \( \boldsymbol{x} \) : \[ -8.1(2 x-2)-x=-10 x+0.9(-10 x+9) \]

To solve the equation \[ -8.1(2x-2)-x=-10x+0.9(-10x+9), \] let's start by simplifying both sides. First, distribute on the left side: \[ -8.1(2x) + 8.1 \cdot 2 - x = -10x + 0.9(-10x + 9). \] This simplifies to: \[ -16.2x + 16.2 - x = -10x + 0.9(-10x) + 0.9 \cdot 9. \] Combine like terms on the left side: \[ -16.2x - x + 16.2 = -10x - 9x + 8.1. \] This gives: \[ -17.2x + 16.2 = -19x + 8.1. \] Next, combine like terms on the right side: Rearranging: \[ -17.2x + 16.2 + 19x = 8.1. \] This simplifies to: \[ 1.8x + 16.2 = 8.1. \] Now, isolate \( x \): \[ 1.8x = 8.1 - 16.2, \] \[ 1.8x = -8.1. \] Now, divide both sides by \( 1.8 \): \[ x = \frac{-8.1}{1.8} = -4.5. \] Thus, the solution is \[ \boxed{-4.5}. \]