Question

three times an odd integer is eleven less than four times the next greater even integer. What is the odd integer?

Answer 1

3(x+2) = 4x-5
3x+ 6 = 4x -5

Subtract 3x from each side:
3x-3x + 6 = 4x-3x -5
6=x-5

Add +5 to each side:
6+5= x-5+5
11=x
x+2= 13.

Answer 2

let the first odd integer be n
then the next even integer is n+1

3n < 4(n+1) by 11
3n = 4(n+1) - 11
3n = 4n + 4 - 11
7 = n

<b>the first odd integer is 7, then next even one is 8</b>

check:
3 times the first = 21
4 times the second = 32
Is 21 eleven less than 32 ??, YES