Solve : `(n+3)/((1)/(3)) - (n+2)/((1)/(2)) = (n-4)/((1)/(10))`. The value of n is obtained as 

Options

A. `-5`
B. 5
C. 6
D. 4

Answer

To solve the equation

\[ \frac{n+3}{\frac{1}{3}} - \frac{n+2}{\frac{1}{2}} = \frac{n-4}{\frac{1}{10}}, \]

we will follow these steps:

### Step 1: Simplify the fractions
We can rewrite the fractions by multiplying by the reciprocal of the denominators:

\[ \frac{n+3}{\frac{1}{3}} = (n+3) \cdot 3 = 3(n+3) = 3n + 9, \]

\[ \frac{n+2}{\frac{1}{2}} = (n+2) \cdot 2 = 2(n+2) = 2n + 4, \]

\[ \frac{n-4}{\frac{1}{10}} = (n-4) \cdot 10 = 10(n-4) = 10n - 40. \]

### Step 2: Substitute back into the equation
Now we substitute these simplified forms back into the equation:

\[ 3n + 9 - (2n + 4) = 10n - 40. \]

### Step 3: Distribute and combine like terms
Distributing the negative sign gives us:

\[ 3n + 9 - 2n - 4 = 10n - 40. \]

Now combine like terms on the left side:

\[ (3n - 2n) + (9 - 4) = 10n - 40, \]

which simplifies to:

\[ n + 5 = 10n - 40. \]

### Step 4: Isolate the variable
Now, we will move all terms involving \(n\) to one side and constant terms to the other side:

\[ 5 + 40 = 10n - n, \]

which simplifies to:

\[ 45 = 9n. \]

### Step 5: Solve for \(n\)
Now, divide both sides by 9:

\[ n = \frac{45}{9} = 5. \]

Thus, the value of \(n\) is

\[ \boxed{5}. \]