Solve the Linear Equation: -3(x+4) - 5x + 5 = 3 - 4(x-2) + 5x

To solve this equation, we will break it down into simpler steps:

$-3(x+4)-5x+5=3-4(x-2)+5x$

• Step 1: Apply the distributive property to both sides.
  Left Side: $-3(x+4) = -3x - 12$
  So, $-3(x+4)-5x+5 = -3x - 12 - 5x + 5$
  Right Side: $-4(x-2) = -4x + 8$
  So, $3 - 4(x-2) + 5x = 3 - 4x + 8 + 5x$

• Step 2: Simplify both sides by combining like terms.
  Left Side: Combine like terms $-3x - 5x - 12 + 5 = -8x - 7$
  Right Side: Combine like terms $-4x + 5x + 3 + 8 = x + 11$

• Step 3: Set the simplified forms equal: $-8x - 7 = x + 11$

• Step 4: Solve for $x$ by manipulating the equation:
  Add $8x$ to both sides: $-7 = 9x + 11$
  Subtract 11 from both sides: $-18 = 9x$
  Divide by 9: $x = -2$

Therefore, the solution to the problem is $x = -2$, which matches choice 2.