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Question 99423: the sum of three consecutive odd integers is the same as the smallest of these integers. what are the smallest of the integers and what is the greatest of these integers?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let x be the smallest of the three consecutive odd integers. The next odd integer is 2 above
that or x + 2, and the next odd integer is 2 above that or x + 2 + 2 which is x + 4. So the
three consecutive odd integers are x, x + 2, and x + 4.
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If you add these three consecutive odd integers together the sum is to equal the smallest
of these odd integers ... that is to say the sum of the three integers is to equal x. In equation
form this becomes:
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x + x + 2 + x + 4 = x
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On the left side, add the x terms and then add the numbers. The result is:
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3x + 6 = x
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Get rid of the x on the right side by subtracting x from both sides to get:
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2x + 6 = 0
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Get rid of the 6 on the left side by subtracting 6 from both sides to change the equation to:
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2x = -6
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Solve for x by dividing both sides by 2 and you get:
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x = -6/2 = -3
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So x, the smallest of the three consecutive odd integers is -3. The next bigger odd integer
is found by adding 2 to get -1. And the final consecutive odd integer is found by adding
2 to -1 to get +1. So the three consecutive odd integers are -3, -1, +1.
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If you add these integers you get -3 and that sum is the same as the smallest of the consecutive
odd integers which is x = -3. The answer checks.
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Hope this helps you to understand the problem.
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