To solve the inequality [tex]\( \Box < -\sqrt{107} < \Box \)[/tex], we need to determine the value of [tex]\(-\sqrt{107}\)[/tex] and identify the closest integers on either side of this value.
1. First, we calculate the square root of 107, which is approximately [tex]\(10.344\)[/tex].
2. Next, we consider the negative of this value, which is approximately [tex]\(-10.344\)[/tex].
3. The integers immediately less than [tex]\(-10.344\)[/tex] and greater than [tex]\(-10.344\)[/tex] are [tex]\(-11\)[/tex] and [tex]\(-10\)[/tex], respectively.
Therefore, we have:
[tex]\[
-11 < -\sqrt{107} < -10
\][/tex]
