Algebra-1

The inequality is: -5 |-n + 7| ≥ -45

Dividing both sides of the inequality by -5, we reverse the inequality sign:

|-n + 7| ≤ 9

Now, we can break it down into two cases:

Case 1: -n + 7 is nonnegative (i.e., -n + 7 ≥ 0)
In this case, the absolute value |-n + 7| is equal to -n + 7, so we have:
-n + 7 ≤ 9

Simplifying this inequality, we get:
-n ≤ 2

Dividing both sides of the inequality by -1 reverses the inequality sign:
n ≥ -2

Case 2: -n + 7 is negative (i.e., ...