To solve this equation, we can first combine the fractions on the left side of the equation by finding a common denominator.

The common denominator between 2 and 7 is 14. We can rewrite the equation as:

(7x + 2x) / 14 = 1

Now, simplify the equation:

9x / 14 = 1

To solve for x, we can multiply both sides by 14 to get rid of the fraction:

9x = 14

Now, divide both sides by 9 to solve for x:

x = 14 / 9

Therefore, x = 1.5556.