Solve: `((3y-4))/2=((5-2y))/4`

Answer

To solve the equation \(\frac{3y - 4}{2} = \frac{5 - 2y}{4}\), we will follow these steps:

### Step 1: Eliminate the fractions
To eliminate the fractions, we can multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 4.

\[ 4 \cdot \frac{3y - 4}{2} = 4 \cdot \frac{5 - 2y}{4} \]

### Step 2: Simplify both sides
Now, simplify both sides:

\[ 2(3y - 4) = 5 - 2y \]

### Step 3: Distribute on the left side
Distributing the 2 on the left side gives us:

\[ 6y - 8 = 5 - 2y \]

### Step 4: Move all terms involving \(y\) to one side
Add \(2y\) to both sides to get all \(y\) terms on one side:

\[ 6y + 2y - 8 = 5 \]

This simplifies to:

\[ 8y - 8 = 5 \]

### Step 5: Move constant terms to the other side
Now, add 8 to both sides:

\[ 8y = 5 + 8 \]

This simplifies to:

\[ 8y = 13 \]

### Step 6: Solve for \(y\)
Finally, divide both sides by 8:

\[ y = \frac{13}{8} \]

### Final Answer
Thus, the solution to the equation is:

\[ y = \frac{13}{8} \]

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