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.
+2666 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 \(3 \times 4 \times 5 \times 6 \times 7 = \color{brown}\boxed{2520}\)
