SOLUTION: The number 9 can be written as the sum of 9 consecutive integers. What is the product of these 9 integers ?

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Question 200929: The number 9 can be written as the sum of 9 consecutive integers. What is the product of these 9 integers ?
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = first integer


So x+1 is the next integer, x+2 is the next integer after that, etc...


So because "The number 9 can be written as the sum of 9 consecutive integers", this means that x%2B%28x%2B1%29%2B%28x%2B2%29%2B%28x%2B3%29%2B%28x%2B4%29%2B%28x%2B5%29%2B%28x%2B6%29%2B%28x%2B7%29%2B%28x%2B8%29=9


x%2B%28x%2B1%29%2B%28x%2B2%29%2B%28x%2B3%29%2B%28x%2B4%29%2B%28x%2B5%29%2B%28x%2B6%29%2B%28x%2B7%29%2B%28x%2B8%29=9 Start with the given equation.


x%2Bx%2B1%2Bx%2B2%2Bx%2B3%2Bx%2B4%2Bx%2B5%2Bx%2B6%2Bx%2B7%2Bx%2B8=9 Remove the parenthesis.


9x%2B36=9 Combine like terms on the left side.


9x=9-36 Subtract 36 from both sides.


9x=-27 Combine like terms on the right side.


x=%28-27%29%2F%289%29 Divide both sides by 9 to isolate x.


x=-3 Reduce.


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Answer:

So the solution is x=-3 which means that the first integer is -3


So the 9 consecutive integers are:

-3, -2, -1, 0, 1, 2, 3, 4, 5


If you multiply them together, you'll get 0 (since 0 is being multiplied here).