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Let x+1 is first odd integer
and x+3 is Second odd integer
3 times of the first integer = 3(x+1)
Twice the second integer=2(x+3)
Condition says
three times the first is 5 more than twice the second
3(x+1)=2(x+3)+5
3x+3=2x+6+5
3x-2x=6+5-3
x=8
First odd integer = x+1=8+1=9
Second odd integer = x+3=8+3=11
Check
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three times the first is 5 more than twice the second
3*9=2*11+5
27=22+5
27=27