Without solving the equations, which absolute value equation has no solution?ResponsesA.   $-\abs{8x-7}-1=6$−8x−7−1=6​A.    negative start absolute value 8 x minus 7 end absolute value minus 1 is equal to 6B.   $\abs{x-7}=0$x−7=0​B.    start absolute value x minus 7 end absolute value is equal to 0C.   $-\abs{3x+5}=-8$−3x+5=−8​C.    negative start absolute value 3 x plus 5 end absolute value is equal to negative 8D.   $\abs{9-6x}+4=12$

The absolute value of a number is always non-negative, meaning it's always greater than or equal to zero. Therefore, an absolute value equation has no solution if the value on the other side of the equation is negative.

Looking at the options:

A. $-\abs{8x-7}-1=6$ can be rewritten as $-\abs{8x-7}=7$. The right side is positive, so this equation could have a solution.

B. $\abs{x-7}=0$ is equal to zero, so this equation has a solution (x=7).

C. $-\abs{3x+5}=-8$ can be rewritten as $\abs{3x+5}=8$. The right side is positive, so this equation could have a solution.

D. $\abs{9-6x}+4=12$ can be rewritten as $\abs{9-6x}=8$. The right side is positive, so this equation could have a solution.

Therefore, none of the given equations have no solution. There might be a mistake in the question or the provided options.