Digit word problems -linear equation

[paulmdrdo1]

can you please tell why my solutions here yield different answers

here's the problem,

Find two consecutive positive odd integers such that the difference of their squares is 64.

my first solution is

let $2x+1=$ smaller odd interger
$2x+3=$ larger odd integer

$(2x+3)^2-(2x+1)^2=64$

$x=9$

the numbers are 19 and 21.

my 2nd solution

let $x=$ smaller odd interger
$x+2=$ larger odd integer

$(x+2)^2-(x)^2=64$

$x=15$

the numbers are 15 and 17.

which solution method is correct?

thanks!

 

[Evgeny.Makarov]

$(2x+3)^2-(2x+1)^2=64$

$x=9$

This should be $x=7$.