Write a compound inequality that represents the following phrase. Graph the solutions. all real numbers that are between -8 and 2, inclusive Write a compound inequality that represents the phrase. Choose the correct answer below. OA. - 8 <= n < 2 OC. - 8 < n < 2 OB. - 8 < n <= 2 OD. - 8 <= n <= 2
The correct compound inequality that represents the given phrase is: (-8 ≤ n) and (n ≤ 2)
Graphically, this can be represented by shading the number line between -8 and 2, including both endpoints.
The correct compound inequality that represents the given phrase is -8 <= n <= 2.
To write a compound inequality that represents the phrase "all real numbers that are between -8 and 2, inclusive," we can break it down into two separate inequalities.
1. The number is greater than or equal to -8: n ≥ -8
This includes -8 itself, as the phrase mentions "inclusive."
2. The number is less than or equal to 2: n ≤ 2
This includes 2 itself, as the phrase mentions "inclusive."
Combining both inequalities, we can write the compound inequality as:
-8 ≤ n ≤ 2
Looking at the options given:
OA. - 8 ≤ n < 2
This option is incorrect because it does not include the value 2, as the phrase requires.
OC. - 8 < n < 2
This option is incorrect because it does not include -8 and 2, as the phrase requires.
OB. - 8 < n ≤ 2
This option is incorrect because it does not include the value -8, as the phrase requires.
OD. - 8 ≤ n ≤ 2
This option is correct because it includes both -8 and 2, as the phrase requires.
Therefore, the correct answer is option OD. - 8 ≤ n ≤ 2.