To solve for x, we need to simplify the equation by combining like terms and isolating x on one side of the equation.

First, let's combine the fractions on the left side of the equation:

X + 4/5 - 2x/3 + 1 = 2x - 1/15

To combine the fractions, we need to find a common denominator. The smallest common denominator for 5 and 3 is 15, so we can rewrite the fractions with that denominator:

3x/15 + 12/15 - 10x/15 + 15/15 = 2x - 1/15

Now we can simplify:

-7x/15 + 27/15 = 2x - 1/15

Next, let's isolate x on one side of the equation. We can do this by adding 7x/15 to both sides:

27/15 = 9x/15 - 1/15

Now we can simplify:

27/15 = 8x/15

Finally, we can solve for x by multiplying both sides by 15/8:

x = 27/8

Therefore, the solution to the equation is x = 27/8.