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.

Guest Aug 16, 2022

#1**0 **

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

BuilderBoi Aug 17, 2022