Final answer:
The range of possible values for the expression 1/x when 7 < x < 13 is 0.0769231... to 0.142857..., corresponding to just above 1/13 to just below 1/7.
Step-by-step explanation:
To find all possible values of the expression 1/x for the interval where 7 < x < 13, we need to consider the behavior of the reciprocal function. As x increases within this range, 1/x will decrease because the reciprocal of a larger number is a smaller number. Thus, when x is at its minimum just above 7, 1/x will be at its maximum just below 1/7. Conversely, when x is at its maximum just below 13, 1/x will be at its minimum just above 1/13.
Therefore, the range of possible values for 1/x when 7 < x < 13 is 0.0769231... (just above 1/13) to 0.142857... (just below 1/7),
The exact range can be expressed as 0.0769231 < 1/x < 0.142857.