which of the following are solutions to the inequality below? select all that apply.$\frac{39}{n}

Question

which of the following are solutions to the inequality below? select all that apply.$\frac{39}{n} < 13$$n = -1$$n = -3$$n = 3$$n = 1$

Accepted Answer

# Explanation: ## Step1: Analyze the inequality for positive $ n $ When $ n>0 $, we can multiply both sides of $ \frac{39}{n}<13 $ by $ n $ (since $ n $ is positive, the inequality sign remains the same) to get $ 39 < 13n $. Then divide both sides by 13: $ \frac{39}{13} 3 $. Wait, but let's check the given positive values: $ n = 3 $ and $ n = 1 $. For $ n = 3 $: $ \frac{39}{3}=13 $, and $ 13<13 $ is false. For $ n = 1 $: $ \frac{39}{1}=39 $, and $ 39<13 $ is false. ## Step2: Analyze the inequality for negative $ n $ When $ n<0 $, multiplying both sides of $ \frac{39}{n}<13 $ by $ n $ (since $ n $ is negative, the inequality sign flips) gives $ 39>13n $. Divide both sides by 13: $ 3 > n $. Since $ n $ is negative, any negative $ n $ will satisfy $ 3 > n $ (because negative numbers are less than 3). Let's check $ n=-1 $: $ \frac{39}{-1}=-39 $, and $ -39<13 $ is true. For $ n = -3 $: $ \frac{39}{-3}=-13 $, and $ -13<13 $ is true. So the correct solutions are $ n=-1 $ and $ n=-3 $, while $ n = 3 $ and $ n = 1 $ are not solutions. # Answer: A. $ n=-1 $ B. $ n=-3 $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Analyze the inequality for positive \( n \)

Step2: Analyze the inequality for negative \( n \)

Answer: