If `3/5p -2 ge 5,` what is the least possible value of `6/5p+2` ?

Options

A. 7
B. 10
C. 16
D. 18

Explanation

To solve the inequality \( \frac{3}{5}p - 2 \geq 5 \) and find the least possible value of \( \frac{6}{5}p + 2 \), we can follow these steps:

### Step 1: Solve the inequality
Start with the given inequality:
\[ \frac{3}{5}p - 2 \geq 5 \]
Add 2 to both sides:
\[ \frac{3}{5}p \geq 5 + 2 \]
\[ \frac{3}{5}p \geq 7 \]

### Step 2: Isolate \( p \)
To isolate \( p \), multiply both sides by \( \frac{5}{3} \):
\[ p \geq 7 \cdot \frac{5}{3} \]
Calculating the right side:
\[ p \geq \frac{35}{3} \]

### Step 3: Find \( \frac{6}{5}p + 2 \)
Now, we need to find the least value of \( \frac{6}{5}p + 2 \). Substitute \( p \) with \( \frac{35}{3} \):
\[ \frac{6}{5}p + 2 = \frac{6}{5} \cdot \frac{35}{3} + 2 \]

### Step 4: Calculate \( \frac{6}{5} \cdot \frac{35}{3} \)
Calculating the first part:
\[ \frac{6 \cdot 35}{5 \cdot 3} = \frac{210}{15} = 14 \]

### Step 5: Add 2
Now, add 2 to the result:
\[ \frac{6}{5}p + 2 = 14 + 2 = 16 \]

### Conclusion
The least possible value of \( \frac{6}{5}p + 2 \) is:
\[ \boxed{16} \]