1/4-2/3y=3/4-1/3y
To solve the equation 1/4 - 2/3y = 3/4 - 1/3y, we can start by gathering the variables on one side and the constants on the other side.
Let's move the y terms to the left side of the equation and the constant terms to the right side:
1/4 + 1/3y - 2/3y = 3/4 - 3/3y
Now, we can combine like terms on both sides of the equation:
1/4 + (1/3 - 2/3)y = 3/4 - 1y
Simplifying further:
1/4 - 1/3y = 3/4 - 1y
Now, let's find a common denominator for the fractions. The least common multiple of 4 and 3 is 12. We can rewrite the equation with a common denominator:
3/12 - 4/12y = 9/12 - 12/12y
Combining like terms again:
(3 - 4y)/12 = (9 - 12y)/12
Since the denominators are the same, we can now equate the numerators:
3 - 4y = 9 - 12y
Now, let's solve for y by isolating the variable on one side of the equation:
-4y + 12y = 9 - 3
Simplifying:
8y = 6
Finally, we can divide both sides of the equation by 8 to solve for y:
y = 6/8
y = 3/4
Therefore, the solution to the equation 1/4 - 2/3y = 3/4 - 1/3y is y = 3/4.