solve:

4x+1/6 + 2x-3/5 = 4/15

To solve the given equation, we first need to simplify the expression on the left side of the equation.

Starting with 4x + 1/6 + 2x - 3/5, we can combine the like terms by adding the coefficients of x. So, 4x + 2x = 6x.

Next, we need to find a common denominator to add the fractions. The common denominator for 6 and 5 is 30. So, we can rewrite the equation as:

(1/6) + (2/5) = (4/15)

To convert the fractions with denominators 6 and 5 to have a common denominator of 30, we multiply the numerator and denominator of (1/6) by 5 and multiply the numerator and denominator of (2/5) by 6:

(5/5) * (1/6) + (6/6) * (2/5) = (4/15)

Simplifying further:

5/30 + 12/30 = 4/15

We can now add the fractions:

(5 + 12)/30 = 4/15

17/30 = 4/15

To solve for x, we need to isolate it on one side of the equation. We can do this by cross multiplying:

15 * 17 = 30 * 4

255 = 120

This is not a true statement, which means there is no solution to the equation.

Therefore, the given equation 4x + 1/6 + 2x - 3/5 = 4/15 has no solution.