To solve this equation, we first need to distribute the coefficients to simplify the expression.

41.4 14/23x = 6.5x
41.4 5/9 = 22.9

79.8 8/19x = 33.6x
79.8 5/6 = 66.5

Therefore, the equation becomes:

6.5x + 22.9 - 33.6x + 66.5 = 76.9

Combine like terms:

-27.1x + 89.4 = 76.9

Subtract 89.4 from both sides:

-27.1x = -12.5

Divide by -27.1 to isolate x:

x = -12.5 / -27.1
x ≈ 0.461

Therefore, the solution to the equation is x ≈ 0.461.