Question

1. \left|2 + 5n\

ight| \geq -8

Explanation:

Step1: Recall absolute value property

The absolute value of any real number \( x \), denoted \( |x| \), is always non - negative. That is, for any real number \( x \), \( |x| \geq 0 \).
In the given inequality \( |2 + 5n|\geq - 8 \), the left - hand side \( |2+5n| \) represents the absolute value of the expression \( 2 + 5n \). Since the absolute value of any real number is greater than or equal to 0, and \( 0\geq - 8 \) (because 0 is to the right of - 8 on the number line), the inequality \( |2 + 5n|\geq - 8 \) will be true for all real numbers \( n \).

Answer:

All real numbers \( n\in(-\infty,\infty) \) (or \( n \) can be any real number)