2х 2х+1 3х-5 ----- - --------- = --------- 3 6 4

To solve this equation, we need to simplify the expression on both sides and then find the value of x.

First, let's simplify the left side of the equation:

2x/3 - (2x + 1)/6

To get a common denominator, we multiply the first term by 2/2 and the second term by 3/3:

(2x/3) * (2/2) - ((2x + 1)/6) * (3/3) = (4x/6) - (6x + 3)/18 = (4x - 6x - 3)/18 = (-2x - 3)/18

Now, let's simplify the right side of the equation:

(3x - 5)/4

Now, we have the following equation:

(-2x - 3)/18 = (3x - 5)/4

To get rid of the denominators, we can multiply both sides of the equation by the product of the denominators, which is 18 * 4 = 72:

72 * (-2x - 3)/18 = 72 * (3x - 5)/4

Simplifying further:

(-8x - 12) * 4 = (216x - 360)/4

-32x - 48 = 54x - 90

To isolate the x variable, let's move the 54x term to the left side and the -48 term to the right side:

-32x - 54x = -90 + 48

-86x = -42

Now, divide both sides of the equation by -86 to solve for x:

x = -42 / -86

x = 21/43

Therefore, the solution to the equation is x = 21/43.