Question

Select the equation has no solution.
Responses
A 2x + 17 - 7x - 6 = 8 - 10x - 19 + 5x
B 7 + 16x + 1 - 4x = 24 + 8x - 9 + 3x
C 9x - 3 + 2x + 20 = 15 + 4x + 2 + 7x
D 12 - 6x + 4 - x = 3 + 8x + 13 - 11x

Answer 1

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**