Given: x/2 y/3 = z/7

To Find: The value of (2x-5y+4z)/2y

Solution:

To find the value of (2x-5y+4z)/2y, we need to simplify the expression using the given equation x/2 y/3 = z/7.

Step 1: Simplify the given equation:

We have x/2 y/3 = z/7

To simplify this equation, we can cross-multiply:

3x * 7 = 2y * z

21x = 2yz

Step 2: Simplify the expression:

Now we can substitute the value of z in the expression (2x-5y+4z)/2y using the equation 21x = 2yz:

(2x-5y+4z)/2y = (2x-5y+4(21x))/2y

Simplifying further:

= (2x-5y+84x)/2y

= (86x-5y)/2y

= 86x/2y - 5y/2y

= 43x/y - 5/2

Final Answer:

Therefore, the value of (2x-5y+4z)/2y is 43x/y - 5/2.

Explanation:

- We started by simplifying the given equation x/2 y/3 = z/7 by cross-multiplying.
- Then, we substituted the value of z in the expression (2x-5y+4z)/2y using the equation 21x = 2yz.
- Finally, we simplified the expression to get the final answer 43x/y - 5/2.