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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.

Solve the following inequality for m. Write your answer in simplest form: 7m - 8 ≥ 8m - 1

Learn how to solve the inequality 7m - 8 ≥ 8m - 1 with a detailed step-by-step solution. This problem involves key algebraic concepts such as inequalities and linear equations. Suitable for students in Grades 7-9.

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