Final answer:
The solution to the equation 5 / 6(x+4) = 5/10 is x = -7/3, achieved by finding a common denominator, distributing, and simplifying.
Step-by-step explanation:
To solve the equation 5 / 6(x+4) = 5/10 for x, we need to find a common denominator to facilitate the solving process. The equation can be simplified by multiplying both sides by 6(x+4) to get rid of the fraction on the left side, giving us 5 = 3(x+4).
Next, we distribute the 3 on the right side to get 5 = 3x + 12. Subtracting 12 from both sides, we obtain -7 = 3x. Finally, dividing both sides by 3, we find that x = -7/3.