Final answer:
The solution to the equation -5/6 = -1/4 - 7/10x is x = 35/42. Step-by-step algebraic manipulation is used to combine fractions, eliminate the fraction on one side, and isolate x. The fraction is simplified to its simplest form.
Step-by-step explanation:
To solve the equation -5/6 = -1/4 - 7/10x, we follow these steps:
- First, find a common denominator for the fractions on the right side of the equation so we can combine them. The smallest common denominator for 4 and 10 is 20. This gives us -5/6 = -5/20 - (14/20)x.
- Combine the terms on the right side of the equation: -5/6 = (-5 - 14x)/20.
- Multiply both sides of the equation by 20 to eliminate the fraction: -5/6 × 20 = (-5 - 14x)/20 × 20, which simplifies to -50/3 = -5 - 14x.
- Add 5 to both sides of the equation to isolate terms with x on one side: -50/3 + 15/3 = -5 + 5 - 14x, simplifying to -35/3 = -14x.
- Finally, divide both sides by -14 to solve for x: x = (-35/3) / (-14) = 35/42.
Thus, the solution for x in the equation -5/6 = -1/4 - 7/10x is x = 35/42, which is the fraction in its simplest form.