Let's solve the given inequality:

$7m - 8 \geq 8m - 1$

Step 1: Simplify both sides.

Start by subtracting $7m$ from both sides to move the terms with $m$ to one side:

$7m - 8 - 7m \geq 8m - 1 - 7m$

This simplifies to:

$-8 \geq m - 1$

Step 2: Solve for $m$.

Now, add 1 to both sides to isolate $m$:

$-8 + 1 \geq m$

Simplifying:

$-7 \geq m$

This is the same as:

$m \leq -7$

Final Answer:

The solution to the inequality is:

$m \leq -7$

Would you like any more details on these steps, or do you have further questions? Here are some related questions to explore:

1. What happens if you multiply or divide both sides of an inequality by a negative number?
2. How do you represent the solution $m \leq -7$ on a number line?
3. Can you explain the difference between $\geq$ and $>$ in inequalities?
4. What are the key steps in solving inequalities involving variables on both sides?
5. How can you check your solution to an inequality?

Tip: When solving inequalities, always remember that reversing the inequality sign is necessary when multiplying or dividing by a negative number.