45x + 160 - 8x = -120 - 3x + 20

To solve the equation \( 45x + 160 - 8x = -120 - 3x + 20 \), we can start by simplifying both sides of the equation.

1. Combine like terms on both sides:

   Left side: \[ 45x - 8x + 160 = 37x + 160 \]

   Right side: \[ -120 + 20 - 3x = -100 - 3x \]

   So the equation now looks like: \[ 37x + 160 = -100 - 3x \]

2. Next, we can add \( 3x \) to both sides to eliminate \( -3x \) from the right side: \[ 37x + 3x + 160 = -100 \] This simplifies to: \[ 40x + 160 = -100 \]

3. Now, subtract \( 160 \) from both sides: \[ 40x = -100 - 160 \] \[ 40x = -260 \]

4. Finally, divide both sides by \( 40 \) to solve for \( x \): \[ x = \frac{-260}{40} \] \[ x = -6.5 \]

Thus, the solution is: \[ x = -6.5 \]