Final answer:
The solution is y = 8/21.
Step-by-step explanation:
To solve the equation 0.5(11/2y-2.5)=1/4y+1.75 for y, we can start by distributing the 0.5 to the terms inside the parentheses.
This gives us 5.5y/4 - 1.25
= 1/4y + 1.75.
We can then combine like terms and isolate the variable y.
Adding 1.25 to both sides gives us 5.5y/4 = 1/4y + 2.
Compare the y terms, and you will find that y has the same denominator on both sides.
By multiplying both sides by 4, we can eliminate the denominators and get 22y = y + 8.
Subtracting y from both sides gives us 21y = 8.
Finally, dividing both sides by 21 gives us y = 8/21.