How would you write (-∞, 4]?

Question

How would you write (-∞, 4] using the greater-than, less-than symbols?

1.) -∞ < x < 4

2.) -∞ ≤ x < 4

3.) -∞ < x ≤ 4

4.) -∞ ≤ x ≤ 4

Please give a reasoning behind your answer, I want to get this! :)

Answer 1

The parenthesis symbol means that the interval does NOT include the equality condition.  The bracket symbol means that the equality condition IS included.  So your interval----from negative infinity to 4 is expressed by choice 3.

Answer 2

3.  This is because x can never be infinity, so x cannot be greater than or equal to infinity because it can never equal infinity (or negative infinity).  4 has the opposite sign, so x is less than or equal to 4.  In reality, it is because the parenthesis means there is no &quot;or equal to,&quot; but this is an easy way to remember.

Answer 3

3)

( means everything except the point

] means everything including the point

Answer 4

The &#039; (&#039; or &#039; )&#039; are used for open intervals and the symbols &#039; [&#039; and &#039;]&#039;

are used for closed intervals.

Open Intervals excludes the endpoints

A Closed inteval includes the endpoints

This interval is open on the left endpoint and closed on the right endpoint.

Therefore the - infinity is not included and the 4 is included.

Thus choice 3

-infinity &lt; x &lt;= 4.

Note: The &quot;equal to&quot; in the less than or equal to includes the 4 in the interval which contrasts the less than sign to the left of -infinity where there is no &quot;equal to&quot; part excluding the negative infinity.

Answer 5

The parenthesis means &lt; and the bracket means ≤:

3.) -∞ &lt; x ≤ 4

Answer 6

( indicates left endpoint not included and ] indicates that

right endpoint IS included.  Thus  

the answer is

-∞ &lt; x ≤ 4 which is choice 3