I cannot seem to work this problem out correctly as all answers found do not make the equation work.

1/4 - 2/3y = 3/4 - 1/3y

Get y on one side alone:

-2/4 = 1/3y

Multiply both sides by 3y to get it out of the denominator:

-6y/4 = 1

multiply both sides by 4:

-6y = 4

Divide both sides by -6

y = -4/6

Check it:

1/4 - 2/(3)(-4/6) = 3/4 - 1/(3)(-4/6)

3*(-4/6) = -12/6 = -2

1/4 - -1 = 3/4 - -(1/2)

1 1/4 = 3/4 + 1/2
1 1/4 = 3/4 + 2/4
1 1/4 = 5/4
1 1/4 = 1 1/4

y = -4/6 or (simplified) -2/3

Matt

Sometimes it helps to get rid of those pesky fractions. Try multiplying both sides by 12 and then working the problem. If you multiply everything on both sides of an equals by the same value it will not change the value of the variable you are trying to find.

The answer is -3/2

To solve this equation, you'll need to combine like terms and isolate the variable y on one side of the equation. Let's go step by step:

Step 1: Common Denominators
To simplify the equation, we need to find a common denominator for the fractions. In this case, we have denominators of 4 and 3. The common denominator for 4 and 3 is 12. Multiply each fraction by the appropriate factor to obtain that denominator.

1/4 becomes (1/4) * (3/3) = 3/12
2/3y becomes (2/3y) * (4/4) = 8/12y
3/4 becomes (3/4) * (3/3) = 9/12
1/3y remains the same.

Now the equation becomes:
3/12 - 8/12y = 9/12 - 1/3y

Step 2: Combining Like Terms
Combine the fractions with the same variables on the left side and the right side of the equation.

(3/12) - (8/12)y = (9/12) - (1/3)y

Step 3: Solving for y
To eliminate the denominators, you can multiply the entire equation by the common denominator, which is 12.

12 * [(3/12) - (8/12)y] = 12 * [(9/12) - (1/3)y]

Now the equation becomes:
3 - 8y = 9 - 4y

Step 4: Isolating the Variable
Rearrange the equation to isolate the variable y on one side.

-8y + 4y = 9 - 3

Combine like terms:
-4y = 6

Step 5: Solving for y
Divide both sides of the equation by -4 to solve for y.

y = 6 / -4

Simplifying the expression:
y = -3/2

Therefore, the solution to the equation is y = -3/2.