To determine which equation has no solution, we can simplify each option and see if they lead to a contradiction.
Option A:
\[ 2x + 17 - 7x - 6 = 8 - 10x - 19 + 5x \]
Combine like terms: \[ -5x + 11 = -10x - 11 + 5x \] \[ -5x + 11 = -5x - 11 \]
Add \( 5x \) to both sides: \[ 11 = -11 \] (This is a contradiction.)
Option B:
\[ 7 + 16x + 1 - 4x = 24 + 8x - 9 + 3x \]
Combine like terms: \[ 8 + 12x = 24 + 11x \]
Subtract \( 11x \) from both sides: \[ 8 + x = 24 \]
Subtract 8 from both sides: \[ x = 16 \]
(This has a solution.)
Option C:
\[ 9x - 3 + 2x + 20 = 15 + 4x + 2 + 7x \]
Combine like terms: \[ 11x + 17 = 15 + 11x \]
Subtract \( 11x \) from both sides: \[ 17 = 15 \]
(This is a contradiction.)
Option D:
\[ 12 - 6x + 4 - x = 3 + 8x + 13 - 11x \]
Combine like terms: \[ 16 - 7x = 16 - 3x \]
Add \( 3x \) to both sides: \[ 16 - 7x = 16 - 3x \]
Subtract 16 from both sides: \[ -7x = -3x \]
Add \( 3x \) to both sides: \[ -4x = 0 \]
This gives \( x = 0 \) (This has a solution.)
Conclusion:
The equations with contradictions (no solutions) are:
- Option A: \( 11 = -11 \)
- Option C: \( 17 = 15 \)
However, as you only asked for one option, Option A is a satisfactory answer since it is the first one.
Final Answer: A