Solve the following inequality for m*m*. Write your answer in simplest form.

7, m, minus, 8, is greater than or equal to, 8, m, minus, 1

7*m*−8≥

8*m*−1 

We are given the inequality:

\[
7m - 8 \geq 8m - 1
\]

We need to solve for \( m \).

### Step 1: Move all terms involving \( m \) to one side.
To do this, subtract \( 7m \) from both sides:

\[
7m - 8 - 7m \geq 8m - 1 - 7m
\]

This simplifies to:

\[
-8 \geq m - 1
\]

### Step 2: Move the constant terms to the other side.
Add 1 to both sides to isolate \( m \) on the right-hand side:

\[
-8 + 1 \geq m
\]

This simplifies to:

\[
-7 \geq m
\]

### Step 3: Rewrite the inequality.
The inequality can be rewritten as:

\[
m \leq -7
\]

### Final Answer:
The solution to the inequality is:

\[
m \leq -7
\]

Would you like any further details, or do you have any questions? 

Here are 5 related questions you can explore:
1. What happens if we reverse the inequality signs?
2. How would the inequality change if the equation were \( 7m - 8 \leq 8m - 1 \)?
3. How can we check the solution by plugging in values of \( m \)?
4. What is the graphical interpretation of this inequality?
5. How would the steps differ for solving an absolute value inequality?

**Tip:** When moving terms across the inequality, make sure to always reverse the inequality sign if you multiply or divide by a negative number.

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

This tutorial explains how to solve the linear inequality 7m - 8 ≥ 8m - 1 step-by-step. Explore key algebra concepts, including inequality manipulation and isolating the variable. Suitable for students in Grades 7-9.

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