y = 13/15
First, write the equation:
1/2 (3/2y+1/3) = -1/2 (y-5/2)
First, distribute 1/2 by multiplying that by 3/2y and 1/3. At the same time, distribute -1/2 by multiplying that by y and -5/2. It should look like:
3/4y + 1/6 = -1/2y + 5/4
When solving to find a variable, you want to get the variable to only one side of the equation. Add 1/2y to both sides of the equation. However, when you have to add 3/4y + 1/2y, you’ll notice that the denominators are different, meaning you have to change them to make the denominators the same. Multiply 1/2 by 2 to get 2/4. Now, add 3/4 + 2/4 to get 5/4. This is what you should now have:
5/4y + 1/6 = 5/4
Next, you want to try and get the variable number by itself. As you can see, 1/6 prevents it from being by itself on one side of the equation. Subtract 1/6 from both sides. Once again, you cannot do this because the denominators aren’t the same. Multiply 5/4 by 6 and 1/6 by 4 to get 30/24 minus 4/24, which equals 26/24. You can now simplify that to 13/12. Now your equation should look like this:
5/4y = 13/12
Divide both sides of the equation by 5/4 to get y = 13/15. That is your final answer. Hope this helped! Sorry if this answer was rlly long lol