Final answer:
To find the value of y that makes the equation 1/4 - 2/3y = 3/4 - 1/3y true, combine like terms and solve for y. The value of y is -3/2.
Step-by-step explanation:
To find the value of y that makes the equation 1/4 - 2/3y = 3/4 - 1/3y true, we need to simplify and solve for y.
First, let's combine like terms on both sides of the equation. We can do this by getting rid of the fractions.
Multiplying both sides by 12 to clear the fractions gives us 3 - 8y = 9 - 4y.
Next, let's isolate the variable y on one side of the equation.
Subtracting -3 from both sides gives us -8y + 4y = 9 - 3, which simplifies to -4y = 6.
Finally, divide both sides by -4 to solve for y. We get y = -6/4
= -3/2.