Thank you for the clarification. Let's solve the inequality:

\[
\frac{15m + 1}{5} \geq \frac{3m - 1}{2}
\]

### Step-by-Step Solution:

1. **Clear the Fractions**:
   To eliminate the fractions, multiply both sides of the inequality by the least common multiple (LCM) of the denominators. The LCM of 5 and 2 is 10.

   Multiply both sides by 10:
   \[
   10 \times \frac{15m + 1}{5} \geq 10 \times \frac{3m - 1}{2}
   \]

2. **Simplify**:
   Simplify the left and right sides:
   \[
   2 \times (15m + 1) \geq 5 \times (3m - 1)
   \]
   Distribute the factors:
   \[
   30m + 2 \geq 15m - 5
   \]

3. **Isolate the Variable (m)**:
   Subtract \(15m\) from both sides to bring the variable terms to one side:
   \[
   30m - 15m + 2 \geq -5
   \]
   Simplify:
   \[
   15m + 2 \geq -5
   \]

   Next, subtract 2 from both sides:
   \[
   15m \geq -7
   \]

4. **Solve for \(m\)**:
   Divide both sides by 15:
   \[
   m \geq \frac{-7}{15}
   \]

### Final Answer:
The solution to the inequality is:
\[
m \geq \frac{-7}{15}
\]

Would you like further details or have any questions?

---

Here are 5 related questions to expand on this topic:

1. How would the solution change if the inequality was strict (i.e., \(>\) instead of \(\geq\))?
2. Can you solve the inequality \(\frac{4m - 5}{3} \leq \frac{2m + 1}{6}\)?
3. How do you handle inequalities where multiplying or dividing by a negative number is required?
4. What if the inequality had a different denominator, such as \(\frac{15m + 1}{7} \geq \frac{3m - 1}{3}\)?
5. How can you check if a value satisfies the inequality?

**Tip**: When solving inequalities, always remember that multiplying or dividing by a negative number reverses the inequality sign.

Learn how to solve the inequality (15m + 1) / 5 >= 3m - 1/2 with a detailed step-by-step solution. This problem covers key algebraic concepts, including inequalities and linear equations involving fractions. Suitable for high school students.

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