Final answer:
The correct absolute value equation that has the solution of x = 17 is option b: |x - 17| = 0. This is verified by substituting x with 17, resulting in |0| = 0, which is true.
Step-by-step explanation:
The question asks us to write an absolute value equation that has the solution of x = 17. The absolute value of a number is its distance from zero on a number line, regardless of direction, hence it is always non-negative. Since we want the solution to be x = 17, the absolute value expression should evaluate to zero when x is replaced by 17, making the contents of the absolute value zero or it should yield x directly when the equation is solved.
The correct option is therefore: b. |x - 17| = 0. Let's verify by substituting x with 17: |17 - 17| = 0, which simplifies to |0| = 0, and since the absolute value of 0 is 0, the equation holds true. None of the other options will result in a true statement when we substitute x = 17.