When `1/7n +3 =(-1)/5(n- 20)`, what is the value of n?

Options

A. `1/12`
B. `35/12`
C. `12/35`
D. 12

Answer

To solve the equation \( \frac{1}{7}n + 3 = -\frac{1}{5}(n - 20) \), we will follow these steps:

### Step 1: Clear the fractions
To eliminate the fractions, we can multiply both sides of the equation by 35, which is the least common multiple of 7 and 5.

\[ 35 \left( \frac{1}{7}n + 3 \right) = 35 \left( -\frac{1}{5}(n - 20) \right) \]

### Step 2: Distribute on both sides
Now, distribute 35 on both sides:

\[ 35 \cdot \frac{1}{7}n + 35 \cdot 3 = 35 \cdot -\frac{1}{5}(n - 20) \]

This simplifies to:

\[ 5n + 105 = -7(n - 20) \]

### Step 3: Distribute on the right side
Now distribute -7 on the right side:

\[ 5n + 105 = -7n + 140 \]

### Step 4: Move all terms involving \( n \) to one side
Add \( 7n \) to both sides:

\[ 5n + 7n + 105 = 140 \]

This simplifies to:

\[ 12n + 105 = 140 \]

### Step 5: Move the constant to the other side
Subtract 105 from both sides:

\[ 12n = 140 - 105 \]

This simplifies to:

\[ 12n = 35 \]

### Step 6: Solve for \( n \)
Now, divide both sides by 12:

\[ n = \frac{35}{12} \]

### Final Answer
Thus, the value of \( n \) is \( \frac{35}{12} \).

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