Question

for the absolute value inequality |n| ≤ 5, which of the following solution sets is correct?
-5 ≤ n ≤ 5 n ≤ -5 or n ≥ 5
all real numbers no solution
for the absolute value inequality |n| > 5, which of the following solution sets is correct?
-5 < n < 5 n < -5 or n > 5
all real numbers no solution
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Explanation:

Step1: Solve $|n| \leq 5$

By absolute value rule, $|x| \leq a$ translates to $-a \leq x \leq a$. Here $a=5$, so:
$-5 \leq n \leq 5$

Step2: Solve $|n| > 5$

By absolute value rule, $|x| > a$ translates to $x < -a$ or $x > a$. Here $a=5$, so:
$n < -5 \text{ or } n > 5$

Answer:

1. For $|n| \leq 5$: $\boldsymbol{-5 \leq n \leq 5}$
2. For $|n| > 5$: $\boldsymbol{n < -5 \text{ or } n > 5}$