Answer:
Option 4: (0, 5]
Step-by-step explanation:
Given the inequality notation, 0 < x ≤ 5 :
Definitions:
open- and closed-parenthesis "( )"
We know that using the open- and closed-parenthesis, "( )" are used to express interval notation for which the endpoints are not included as part of the solution. Hence, the open- and closed-parenthesis are associated with the inequality symbols, less than (>) or greater than (<), as you do not include the endpoints when these inequality symbols are used.
open- and closed-brackets "[ ]"
In contrast, the open- and closed-brackets, "[ ]" are used to express interval notation for which the endpoints are included as part of the solution. Hence, the open- and closed-parenthesis are associated with the inequality symbols, less than or equal to (≤), and greater than or equal to (≥).
Step-by-step explanation:
In the inequality notation, 0 < x ≤ 5, the endpoints are 0 and 5.
The inequality symbol between 0 and x is "<," which means that we must use an open parenthesis, " ( " for the endpoint, 0.
While the inequality symbol between x and 5 is "≤," which means that we must use an closed bracket, " ] " for the endpoint, 5.
Therefore, the correct answer is Option 4: (0, 5].