1/3÷(3/7×x-13/45)=1 9/16

First, we need to simplify the expression on the left side of the equation:

1/3 ÷ (3/7)x - 13/45 = 1 9/16

1/3 ÷ (3/7)x = 1 9/16 + 13/45
1/3 ÷ (3/7)x = 25/16 + 13/45

Now we can find a common denominator and add the fractions on the right side of the equation:

1/3 ÷ (3/7)x = (25/16) (45/45) + (13/45) (16/16)
1/3 ÷ (3/7)x = 1125/720 + 208/720
1/3 ÷ (3/7)x = 1333/720

Now we can solve for x:

1/3 ÷ (3/7)x = 1333/720
1/3 (7/3)x = 1333/720
7x/9 = 1333/720
7x = 1333/720 9
7x = 11997/720
x = 11997/720 / 7
x = 1714/120
x = 14 1/5

Therefore, the solution to the equation is x = 14 1/5.