To solve this equation, we first need to simplify both sides of the equation.

1/2 x - 3/4 = 14/9 × 3/7

First, simplify the right side of the equation by multiplying the fractions:

14/9 × 3/7 = (14 × 3) / (9 × 7) = 42 / 63 = 2/3

Now, the equation becomes:

1/2 x - 3/4 = 2/3

Next, we need to get rid of the fractions by finding a common denominator. The common denominator for 2, 3, and 4 is 12.

Multiplying each term by 12, we get:

6x - 9 = 8

Now, we can solve for x:

6x = 17

x = 17 / 6

Therefore, the solution to the equation is x = 17 / 6.