SOLUTION: the 1st and 3rd of three consective integers are odd integers are added, the result is 69 less than five times the second integer. Find the third integer familiarize with steps

Question 293274: the 1st and 3rd of three consective integers are odd integers are added, the result is 69 less than five times the second integer. Find the third integer
familiarize with steps
x = odd integer
x + 2 = 2nd Odd Integer
x + 4 = 3rd Odd integer
Translate
x + (x + 4) is 1st PLUS 3rd integer
69 - 5(x + 2) is 69 less than 5 times the 2nd integer
the 1st odd integer plus the 3rd consective odd integer [x + (x+4)] equals the sum of 69 less than 5(x + 2) the 2nd integer
x + (x + 4 ) = 69 - 5(x + 2)
2x + 4 = 69 - 5x - 10
2x + 4 = 59 - 5x
2x = 55 - 5x
7x = 55
This does not get me a whole number to test the answer for odd consective integers.
Where have I gone wrong?

Found 3 solutions by jim_thompson5910, stanbon, jello3211:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Your error lies in the translation. The first one is fine, but the second expression should be .

So your equation should be
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
the 1st and 3rd of three consective integers are odd integers are added, the result is 69 less than five times the second integer.
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Even numbers are always multiples of 2 and must be represented as 2x,2(x+1),etc.
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Odd numbers are one less than an even or one greater than an even number:
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Let 1st be 2x-1
then 2nd is 2x+1
and 3rd is 2x+3
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Equation:
(2x-1)+(2x+3) = 5(2x+1)-69
4x+2 = 10x-64
6x = 66
x = 11
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1st is 2x-1 = 21
2nd is 2x+1 = 23
3rd is 2x+3 = 25
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Cheers,
Stan H.
Answer by jello3211(7)   (Show Source): You can put this solution on YOUR website!

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