Final answer:
The equation |-x+9|=0 has no solution for any x except for x=9, which makes the equation true. Without additional context or conditions that demand no solution for all x, this typically indicates a typo or miscommunication in the problem statement.
Step-by-step explanation:
The student's question pertains to identifying which of the given equations has no solution. An equation will have no solution if, after simplifying, you are left with a statement that is false (such as a positive number equaling zero). In this case, the equation that has no solution is |-x+9|=0. This is because the absolute value of any real number is always either zero or positive. Since -x + 9 will be a positive number unless x is 9, for all other values of x, the equation yields a positive result not equal to zero. Thus, the equation has no solution for any value of x other than 9, but when x is 9, it simplifies to |-9 + 9| = |0| = 0, which does have a solution. However, if this equation is intended to represent no solution for all possible x, it would imply a typo missing additional context or a special condition. If that's the case, it's usually due to problems with writing the absolute value expression correctly and would suggest that the correct form of the question has been lost in translation. If no such condition exists, then |-x+9|=0 indeed has the solution x=9, and the question was not stated correctly.