What value of n satisfies the equation `7/8 (n-6)=(21)/(2)` ?

Explanation

To solve the equation \( \frac{7}{8} (n - 6) = \frac{21}{2} \), we will follow these steps:

### Step 1: Eliminate the fraction on the left side
To eliminate the fraction, we can multiply both sides of the equation by 8 (the denominator of the left side):

\[ 8 \cdot \frac{7}{8} (n - 6) = 8 \cdot \frac{21}{2} \]

This simplifies to:

\[ 7(n - 6) = 84 \]

### Step 2: Distribute on the left side
Next, we distribute the 7 on the left side:

\[ 7n - 42 = 84 \]

### Step 3: Isolate the term with \( n \)
Now, we will isolate the term with \( n \) by adding 42 to both sides:

\[ 7n - 42 + 42 = 84 + 42 \]

This simplifies to:

\[ 7n = 126 \]

### Step 4: Solve for \( n \)
Finally, we divide both sides by 7 to solve for \( n \):

\[ n = \frac{126}{7} \]

Calculating this gives:

\[ n = 18 \]

Thus, the value of \( n \) that satisfies the equation is \( n = 18 \).

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