SOLUTION: Find all sets of three consecutive positive odd integers whose sum is less than 20 but greater than 10. * Could you please provide the original equation used in this problem. T

Algebra ->  Inequalities -> SOLUTION: Find all sets of three consecutive positive odd integers whose sum is less than 20 but greater than 10. * Could you please provide the original equation used in this problem. T      Log On


   



Question 104959This question is from textbook Algebra 2 with trigonometry
: Find all sets of three consecutive positive odd integers whose sum is less than 20 but greater than 10.
* Could you please provide the original equation used in this problem. Thank you.
This question is from textbook Algebra 2 with trigonometry

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.x%2B%28x%2B2%29%2B%28x%2B4%29%3E10
2.x%2B%28x%2B2%29%2B%28x%2B4%29%3C20
From 1,
3x%2B6%3E10
3x%3E4
x%3E4%2F3
From 2,
3x%2B6%3C20
3x%3C14
x%3C14%2F3
Remember x must be a positive odd integer.
Let's refine our inequalities by finding the closest even integer as limit.
x%3E4%2F3
x%3E2
and
x%3C14%2F3
x%3C4
The only positive odd integer that satisfies both requirements is
x=3
3,5,7 is the only set.
Let's verify.
10%3C3%2B5%2B7%3C20
10%3C15%3C20
Good answer.