To solve the first equation:

7x - 9/12 = 35/84

First, simplify both sides of the equation by converting all fractions to have a common denominator:

7x - 3/4 = 5/12

Now, multiply both sides of the equation by 12 to eliminate the fraction:

12(7x - 3/4) = 12(5/12)

84x - 9 = 5

Add 9 to both sides:

84x = 14

Divide by 84 to solve for x:

x = 14/84
x = 1/6

So, the solution to the first equation is x = 1/6.

To solve the second equation:

2x + 7/17 = 60/68

First, simplify both sides of the equation by converting all fractions to have a common denominator:

2x + 4/17 = 15/17

Now, subtract 4/17 from both sides of the equation:

2x = 15/17 - 4/17
2x = 11/17

Divide by 2 to solve for x:

x = 11/34

So, the solution to the second equation is x = 11/34.