Question

Solve -3y + 7/4y = -2 -5/4y - 1 for y?

A) y=−3
B) y=0
C) y=−6
D) Infinite solutions
E) No solution

Answer 1

To solve the equation -3y + 7/4y = -2 - 5/4y - 1 for y, combine like terms and isolate the variable. The solution is y = 1/23.

Step-by-step explanation:

To solve the equation -3y + 7/4y = -2 - 5/4y - 1 for y, we need to combine like terms and isolate the variable y. Here are the steps:

1. Distribute the negative sign to all terms on the right side of the equation: -2 - 5/4y - 1 = -2 - (5/4)y - 1 = -2 - 5/4y - 4/4 = -2 - 5/4y - 9/4.
2. Combine like terms: -15/4y - 11/4 = -15/4y - 11/4.
3. Bring y terms to one side and constant terms to the other side of the equation: -3y + (7/4y + 15/4y) = -9/4 + 11/4.
4. Combine the y terms: (-3 + 7/4 + 15/4)y = 2/4.
5. Combine the constant terms: -3/4 = 2/4.
6. Solve for y by dividing both sides of the equation by the coefficient of y: y = 2/4 / (5/4 + 15/4 + 3).
7. Simplify: y = 2/4 / (23/4) = 2/4 * 4/23 = 1/23.

Therefore, the solution for y is y = 1/23.