To find this out we can set the expressions equal to each other:
[tex]\sf 2(x+3)=3(x+1)[/tex]
Solve for 'x', first distribute:
[tex]\sf 2x+6=3x+3[/tex]
Subtract 3 to both sides:
[tex]\sf 2x+3=3x[/tex]
Subtract 2x to both sides:
[tex]\boxed{\sf x=3}[/tex]
So the answer is yes, after 3 weeks the dogs will be the same weight(because 'x' represents # of weeks).