Final answer:
The proper absolute value inequality to represent the verbal statement is |x-5| < 13, which ensures that the distance from 5 is less than 13, aligning with one part of the range given in the verbal statement.
Step-by-step explanation:
To represent the verbal statement, 'The set of all real numbers x for which the distance from 0 to 5 is more than half but less than 13,' we need to write an absolute value inequality. This statement means we are looking for values of x such that when you take the absolute value of the distance between x and 5, it falls within the specified range. Since 'more than half' is 0.5, we adjust this to a more practical whole number, resulting in an inequality where the absolute value must be greater than 0.5 but less than 13.
However, when writing absolute value inequalities, it is common practice to use whole numbers. Therefore, the correct answer is not explicitly given in the options as the values are 6.5 and 13. So, we must choose from the provided options in the question. Given that 13 is directly mentioned as the upper bound, we should focus on that. Therefore, the correct inequality would ensure the absolute distance from 5 is less than 13.
The inequality would be: |x-5| < 13
This satisfies the condition by ensuring that the distance from 5 is always less than 13, but does not account for the 'more than half' part as none of the options addresses this side of the condition. Hence, the most suitable answer from the given options is: (d) |x-5| < 13.