If `3p-2ge1` , what is the least possible value of 3p +2 ?

Options

A. 5
B. 3
C. 2
D. 1

Explanation

To solve the problem, we need to find the least possible value of \(3p + 2\) given the inequality \(3p - 2 \geq 1\).

### Step-by-step Solution:

1. **Start with the given inequality**:
\[ 3p - 2 \geq 1 \]

2. **Add 2 to both sides of the inequality**:
\[ 3p - 2 + 2 \geq 1 + 2 \]
This simplifies to:
\[ 3p \geq 3 \]

3. **Divide both sides by 3**:
\[ \frac{3p}{3} \geq \frac{3}{3} \]
This simplifies to:
\[ p \geq 1 \]

4. **Now, substitute \(p\) back into the expression \(3p + 2\)**:
To find the least value of \(3p + 2\), we substitute the minimum value of \(p\) which is 1:
\[ 3(1) + 2 = 3 + 2 = 5 \]

5. **Conclusion**:
Therefore, the least possible value of \(3p + 2\) is:
\[ \boxed{5} \]