Question

Solve for y: x = (6y + 10) / (2y + 3). I just need to understand the steps. I forgot how to solve for y like this.

A. y = (3x - 10) / (6 - x)
B. y = (10 - 3x) / (x + 6)
C. y = (10 - x) / (6 - 3x)
D. y = (x - 10) / (6 + 3x)

Answer 1

To solve for y in the equation x = (6y + 10) / (2y + 3), you need to multiply both sides by the denominator, rearrange terms to get y on one side, factor y out, and then divide the entire equation by the term multiplied by y.

Step-by-step explanation:

To solve for y in the equation x = (6y + 10) / (2y + 3), follow these steps:

1. Multiply both sides of the equation by the denominator on the right side to eliminate the fraction:
2. x * (2y + 3) = 6y + 10
3. Expand the left side: 2xy + 3x = 6y + 10
4. Get all the terms with y on one side and the constant terms on the other: 2xy - 6y = 10 - 3x
5. Factor out y on the left side: y(2x - 6) = 10 - 3x
6. Finally, divide both sides by (2x - 6) to isolate y: y = (10 - 3x) / (2x - 6)

This results in option B: y = (10 - 3x) / (x + 6) after simplifying the right side denominator.