To solve this equation, we first need to find a common denominator for all the fractions on the left side of the equation. The common denominator in this case is 14.

So, we rewrite the equation with a common denominator:

(2(3X-5))/14 + (2X+1)/14 = (7(2X-3))/14

Now we combine the fractions:

(6X - 10 + 2X + 1) / 14 = (14X - 21) / 14

Simplify the equation further:

8X - 9 = 14X - 21

Move all terms involving X to one side of the equation:

8X - 14X = -21 + 9

Combine like terms:

-6X = -12

Divide by -6 to solve for X:

X = 2

Therefore, the solution to the equation is X = 2.