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 What is the product of all positive integers n that satisfy the inequalities 3n + 8 < 30 and 2n - 9 > -4?

 

Hey. Pls solve this CPhil or Melody. I need help.

 

 

Ok, so I tried to make it into a triple inequality after simplifying like this 

 

2.5 < n < 12.66666667 

To get 3,4,5,6,7,8,9,10,11,12.

Mulitplying all those didn't work.

 

So I tried doing each one individualy and go the same answer.

 

I dont know where I went wrong.

 Aug 16, 2022
 #1
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Inequality 1: \(3n + 8< 30\)

 

Subtract 8 from both sides: \(3n <22\)

 

Divide by 3: \(n < {22 \over 3}\)

 

 

Inequality 2: \(2n - 9 > -4\)

 

Add 9 to both sides: \(2n > 5\)

 

Divide both sides by 2: \(n > {5 \over 2}\)

 

So our range becomes \({5 \over 2} < n < {22 \over 3}\)

 

The integers that work are 3, 4, 5, 6, and 7.

 

So the answer is \(3 \times 4 \times 5 \times 6 \times 7 = \color{brown}\boxed{2520}\)

 Aug 17, 2022

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