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The given inequality is:

\[
2m - 1 \geq 5 \quad \text{or} \quad 5m \geq -25.
\]

We will solve each part of the inequality separately.

### First inequality: \( 2m - 1 \geq 5 \)

1. Add 1 to both sides:
   \[
   2m \geq 5 + 1
   \]
   \[
   2m \geq 6
   \]

2. Divide both sides by 2:
   \[
   m \geq 3
   \]

### Second inequality: \( 5m \geq -25 \)

1. Divide both sides by 5:
   \[
   m \geq \frac{-25}{5}
   \]
   \[
   m \geq -5
   \]

### Solution

The solution is the union of these two inequalities:

\[
m \geq 3 \quad \text{or} \quad m \geq -5
\]

Since the second part is redundant (as \( m \geq 3 \) includes values greater than or equal to \(-5\)), the final solution is:

\[
m \geq -5
\]

Let me know if you'd like more details or have any questions. Here are 5 related questions you might find useful:

1. How would you graph the solution of this inequality on a number line?
2. What happens if the inequalities were combined with "and" instead of "or"?
3. How do you solve compound inequalities involving "and"?
4. Can you solve an inequality involving absolute values?
5. How do the solutions of linear inequalities change if you multiply or divide by a negative number?

**Tip:** When solving inequalities, always remember to reverse the inequality sign if you multiply or divide by a negative number!

Solve the inequality 2m - 1 >= 5 or 5m >= -25.

Learn how to solve the linear inequalities 2m - 1 >= 5 and 5m >= -25 step-by-step. This problem covers key algebraic concepts and properties of inequalities, suitable for students in Grades 7-9.

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