SOLUTION: The larger of 2 consecutive integers is eleven more than one-half of the smaller. Find all of the integers. Thanks so much in advance!

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Question 342693: The larger of 2 consecutive integers is eleven more than one-half of the smaller.
Find all of the integers.

Thanks so much in advance!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"The larger of 2 consecutive integers is eleven more than one-half of the smaller.
Find all of the integers." means that x%2B1=%281%2F2%29x%2B11 where 'x' is the first integer and 'x+1' is the second integer (ie 'x+1' is larger than 'x')


x%2B1=%281%2F2%29x%2B11 Start with the given equation.


2%28x%2B1%29=2%28%281%2Fcross%282%29%29x%2B11%29 Multiply both sides by the LCD 2 to clear any fractions.


2x%2B2=x%2B22 Distribute and multiply.


2x=x%2B22-2 Subtract 2 from both sides.


2x-x=22-2 Subtract x from both sides.


x=22-2 Combine like terms on the left side.


x=20 Combine like terms on the right side.


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Answer:

So the solution is x=20


This means that the first integer is 20 and the second integer is 21.


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Jim