Solving the Equation 7y-3 / 9y-5 = 2/3: Step-by-Step Guide

To solve for y, we will first simplify the equation:

7y - 3 / 9y - 5 = 2 / 3

To simplify the left side of the equation, we need to find a common denominator for 3 and 9y. The common denominator is 3(3y) = 9y. We can multiply the numerator and denominator of the first fraction by 3 to get a common denominator:

(7y - 3 * 3) / (9y - 5) = 2 / 3

(7y - 9) / (9y - 5) = 2 / 3

Now, we can cross-multiply to get rid of the fractions:

3(7y - 9) = 2(9y - 5)

21y - 27 = 18y - 10

Next, we will isolate the y term on one side of the equation by subtracting 18y from both sides:

21y - 18y - 27 = 18y - 18y - 10

3y - 27 = -10

To isolate the constant term, we will add 27 to both sides:

3y - 27 + 27 = -10 + 27

3y = 17

Finally, we can solve for y by dividing both sides by 3:

3y / 3 = 17 / 3

y = 17 / 3