Q. \(-2x + 5(x – 4) – 3(2x – 3) = 10\).

Step-by-step solution

1. Start with the given equation.
   \[ -2x + 5(x – 4) – 3(2x – 3) = 10 \]
2. Distribute the multiplication across each parenthesis. Multiply 5 by each term in (x − 4), and −3 by each term in (2x − 3).
   \[ 5(x – 4) = 5x – 20 \]
   \[ -3(2x – 3) = -6x + 9 \]
   Substitute these into the equation:
   \[ -2x + (5x – 20) + (-6x + 9) = 10 \]
3. Remove the parentheses (they are not needed after distribution) and write all terms explicitly:
   \[ -2x + 5x – 20 – 6x + 9 = 10 \]
4. Combine like terms. First combine the x-terms:
   \[ -2x + 5x – 6x = (-2 + 5 – 6)x = -3x \]
   Then combine the constant terms:
   \[ -20 + 9 = -11 \]
   So the equation becomes:
   \[ -3x – 11 = 10 \]
5. Isolate the term with x by removing the constant on the left. Add 11 to both sides (this keeps the equality balanced):
   \[ -3x – 11 + 11 = 10 + 11 \]
   Simplify:
   \[ -3x = 21 \]
6. Solve for x by dividing both sides by −3 (again keeping the equality balanced):
   \[ x = \frac{21}{-3} \]
   Simplify the fraction:
   \[ x = -7 \]
7. Check the solution by substituting x = −7 back into the original equation. Compute each part:
   \[ -2x = -2(-7) = 14 \]
   \[ 5(x – 4) = 5(-7 – 4) = 5(-11) = -55 \]
   \[ -3(2x – 3) = -3(2(-7) – 3) = -3(-14 – 3) = -3(-17) = 51 \]
   Sum these results:
   \[ 14 + (-55) + 51 = 14 – 55 + 51 = 10 \]
   The right-hand side is 10, which matches the original right-hand side, so the solution is correct.

Solution: x = -7