Let's solve the inequality step by step.

The inequality is:

\[
8m - 3(10m - 10) < 9m + 1 + 7
\]

### Step 1: Expand the expression

Distribute the \(-3\) across the terms inside the parentheses:

\[
8m - 3(10m) + 3(10) < 9m + 1 + 7
\]

This gives us:

\[
8m - 30m + 30 < 9m + 8
\]

### Step 2: Combine like terms

On the left-hand side, combine \(8m\) and \(-30m\):

\[
-22m + 30 < 9m + 8
\]

### Step 3: Move all terms involving \(m\) to one side

Subtract \(9m\) from both sides:

\[
-22m - 9m + 30 < 8
\]

\[
-31m + 30 < 8
\]

### Step 4: Move constant terms to the other side

Subtract 30 from both sides:

\[
-31m < 8 - 30
\]

\[
-31m < -22
\]

### Step 5: Solve for \(m\)

Divide both sides by \(-31\), remembering to flip the inequality sign:

\[
m > \frac{-22}{-31}
\]

\[
m > \frac{22}{31}
\]

### Final solution:
\[
m > \frac{22}{31}
\]

This means that the solution to the inequality is \(m > \frac{22}{31}\).

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

Here are 5 related questions you could explore:
1. How do you solve a system of linear inequalities?
2. How do you solve inequalities involving absolute values?
3. What happens when you multiply or divide both sides of an inequality by a negative number?
4. How do you graph the solution to an inequality on a number line?
5. How does solving an inequality differ from solving an equation?

**Tip:** Always flip the inequality sign when multiplying or dividing both sides by a negative number.

Learn how to solve the inequality 8m - 3(10m - 10) < 9m + 1 + 7 step by step. This problem uses key algebraic concepts such as the distributive property and inequality rules. The solution involves solving for m, yielding m > 22/31. Ideal for students in Grades 8-10.

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