The given inequality is:

\[
7r - 10 > 8r + 3
\]

To solve for \(r\), follow these steps:

1. Subtract \(8r\) from both sides to group the variable terms on one side:

\[
7r - 8r - 10 > 8r - 8r + 3
\]

This simplifies to:

\[
-r - 10 > 3
\]

2. Add 10 to both sides to isolate the term with \(r\):

\[
-r - 10 + 10 > 3 + 10
\]

This simplifies to:

\[
-r > 13
\]

3. Multiply both sides by \(-1\) and remember to flip the inequality sign:

\[
r < -13
\]

Thus, the solution to the inequality is:

\[
r < -13
\]

### Would you like any further clarification or details?

Here are 5 related questions you might want to explore:
1. How do you solve inequalities involving fractions?
2. What happens when inequalities include absolute values?
3. How do you represent the solution to this inequality on a number line?
4. Can you apply similar steps to solve compound inequalities?
5. How does multiplying or dividing by negative numbers affect inequalities?

**Tip**: Always remember to flip the inequality sign when multiplying or dividing by a negative number!

Learn how to solve the linear inequality 7r - 10 > 8r + 3 step-by-step. This problem focuses on key algebraic concepts, including solving inequalities and the rules for flipping inequality signs when multiplying by negative numbers. Suitable for students in Grades 8-10.

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