`(9n-(5n-3))/(8)=(2(n-1)-(3-7n))/(12)`
In the equation above, what is the value of n?

Answer

To solve the equation \((9n - (5n - 3))/(8) = (2(n - 1) - (3 - 7n))/(12)\), we will follow these steps:

### Step 1: Simplify both sides of the equation
Start by simplifying the left side:
\[ 9n - (5n - 3) = 9n - 5n + 3 = 4n + 3 \]
So, the left side becomes:
\[ \frac{4n + 3}{8} \]

Now simplify the right side:
\[ 2(n - 1) - (3 - 7n) = 2n - 2 - 3 + 7n = 2n + 7n - 2 - 3 = 9n - 5 \]
So, the right side becomes:
\[ \frac{9n - 5}{12} \]

Now, our equation looks like this:
\[ \frac{4n + 3}{8} = \frac{9n - 5}{12} \]

### Step 2: Cross-multiply
Cross-multiply to eliminate the fractions:
\[ 12(4n + 3) = 8(9n - 5) \]

### Step 3: Distribute
Distributing both sides gives:
\[ 48n + 36 = 72n - 40 \]

### Step 4: Move all terms involving \(n\) to one side
Rearranging the equation:
\[ 48n + 36 + 40 = 72n \]
This simplifies to:
\[ 48n + 76 = 72n \]

### Step 5: Isolate \(n\)
Now, isolate \(n\) by moving \(48n\) to the right:
\[ 76 = 72n - 48n \]
This simplifies to:
\[ 76 = 24n \]

### Step 6: Solve for \(n\)
Now, divide both sides by 24:
\[ n = \frac{76}{24} \]
This can be simplified:
\[ n = \frac{19}{6} \]

### Final Answer
Thus, the value of \(n\) is:
\[ \boxed{\frac{19}{6}} \]

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