Without solving the equations, which absolute value equation has no solution?
A. $-|8 x-7|-1=6$
B. $|x-7|=0$
C. $-|3 x+5|=-8$
D. $|9-6 x|+4=12$
\boxed{\text{Final Answer: A. } -|8 x-7|-1=6}
Step 1 :Analyze each equation to determine if it has a solution or not.
Step 2 :A. $-|8 x-7|-1=6$ has no solution because the left side will always be less than or equal to -1, while the right side is 6.
Step 3 :B. $|x-7|=0$ has a solution (x = 7) because the absolute value can be zero if the expression inside is zero.
Step 4 :C. $-|3 x+5|=-8$ has a solution because the left side will always be less than or equal to 0, and the right side is -8.
Step 5 :D. $|9-6 x|+4=12$ has a solution because the left side will always be greater than or equal to 4, and the right side is 12.
Step 6 :\boxed{\text{Final Answer: A. } -|8 x-7|-1=6}