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2 years ago

PLEASE HELPPPP. I really need it

Mathematics

1 answer:

GalinKa [24]2 years ago

5 0

Answer:

Option 4: (0, 5]

Step-by-step explanation:

Given the <u>inequality notation</u>, 0 < <em>x</em> ≤ 5 :

<h2><u>Definitions:</u></h2><h3>open- and closed-parenthesis "( )"</h3>

We know that using the <u>open- and closed-parenthesis</u>, "( )" are used to express interval notation for which the endpoints are <em><u>not</u></em> included as part of the solution. Hence, the open- and closed-parenthesis are associated with the inequality symbols, <em>less than </em>(>) or greater than (<), as you do not include the endpoints when these inequality symbols are used.

<h3>open- and closed-brackets "[ ]"</h3>

In contrast, the <u>open- and closed-brackets</u>, "[ ]" are used to express interval notation for which the endpoints <u><em>are</em></u> included as part of the solution. Hence, the open- and closed-parenthesis are associated with the inequality symbols, <em>less than or equal to </em>(≤), and <em>greater than</em><em> </em><em>or equal to</em> (≥).

<h2><u>Explanation:</u></h2>

In the inequality notation, 0 < <em>x</em> ≤ 5, the endpoints are 0 and 5.

The inequality symbol <u>between 0 and x</u> is "<," which means that we must use an open parenthesis, " ( " for the endpoint, 0.

While the inequality symbol <u>between x and 5</u> is "≤," which means that we must use an closed bracket, " ] " for the endpoint, 5.

Therefore, the correct answer is Option 4: (0, 5].

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