Final answer:
The solution x > 2/3 is correctly represented by the interval notation (2/3, ∞), which indicates that x is greater than 2/3 and extends indefinitely, without including the endpoints.
Step-by-step explanation:
The solution to an inequality given in set-builder notation as x > 2/3 corresponds to all the values of x that are greater than 2/3, but not including 2/3 itself. This can be represented on a number line where the interval starts just after 2/3 and extends to infinity. Option (c) (2/3, ∞) is the correct representation of this interval because it signifies that x is greater than 2/3 and continues indefinitely to the right on the number line.
The notation used here means that the interval is open at 2/3 (indicated by the parenthesis), so 2/3 is not included in the set, and it is also open at infinity because a set cannot include infinity.