List the integers that can replace n to make the statement -|8| < n < or = to
- |-5| true.
{-7,-6,-5}
True
To answer this question, we need to understand the concept of absolute value and inequalities.
Absolute value is a mathematical function that gives the distance of a number from zero on a number line. It is denoted by the symbol "| |".
In this case, we have the inequality -|8| < n ≤ -|-5|. Let's break it down step by step:
1. First, let's simplify the absolute value expressions:
-|8| = -8, because the absolute value of 8 is 8.
-|-5| = -(-5) = 5, because the absolute value of -5 is 5.
2. Now we have the simplified inequality:
-8 < n ≤ 5.
To find the integers that make this statement true, we need to find the values of n that satisfy this inequality.
Starting from -8, we can list the integers in increasing order until we reach 5. So, the integers that can replace n and make the statement true are:
-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, and 5.
Therefore, the integers that satisfy the inequality -|8| < n ≤ -|-5| are -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, and 5.