Final answer:
After solving the equation -2x - 7y = y - 4x, we find that x = 5y. Option D is correct.
Step-by-step explanation:
The student asks to solve for x in the equation -2x - 7y = y - 4x. To solve for x, we first simplify the equation by collecting like terms. Here are the steps:
Add 4x to both sides: -2x + 4x - 7y = y + 0.
Simplify the equation: 2x - 7y = y.
Now, add 7y to both sides: 2x = y + 7y.
Combine like terms: 2x = 8y.
Finally, divide both sides by 2: x = 5y.
However, none of the given options (a) x = -3y, (b) x = 3y, (c) x = -5y, or (d) x = 5y match the result x = 5y. Therefore, it appears there might be an error either in the given options or in the original equation provided by the student.
To solve for x in the equation -2x - 7y = y - 4x, we need to isolate x on one side of the equation.
First, let's simplify the equation by combining like terms.
Starting with the left side of the equation: -2x - 7y.
Next, we'll simplify the right side of the equation: y - 4x.
Now, let's bring the variables and constants to separate sides of the equation.
Move the terms with x to the left side: -2x + 4x = y + 7y.
Combine the x terms: 2x = 8y.
Divide both sides of the equation by 2 to solve for x: x = 5y.