Let's solve the inequality step by step:

Given inequality:

\[
5y + 6y - 81 < 7y + 102 + 65y
\]

1. **Combine like terms on both sides:**

   - On the left side: \( 5y + 6y = 11y \), so the inequality becomes:
     \[
     11y - 81 < 7y + 65y + 102
     \]
   - On the right side: \( 7y + 65y = 72y \), so the inequality becomes:
     \[
     11y - 81 < 72y + 102
     \]

2. **Move the variable terms to one side and the constant terms to the other:**

   - Subtract \( 11y \) from both sides:
     \[
     -81 < 72y - 11y + 102
     \]
   - Simplify:
     \[
     -81 < 61y + 102
     \]

   - Subtract 102 from both sides:
     \[
     -81 - 102 < 61y
     \]
   - Simplify:
     \[
     -183 < 61y
     \]

3. **Solve for \( y \):**

   - Divide both sides by 61:
     \[
     \frac{-183}{61} < y
     \]

   - Simplify:
     \[
     -3 < y
     \]

**Final solution:**

\[
y > -3
\]

Would you like a detailed explanation of any steps or have any questions?

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Here are 8 related questions:

1. How do you solve an equation with variables on both sides?
2. What are the steps to solve a linear inequality?
3. How do you combine like terms in an equation or inequality?
4. What happens when you divide or multiply both sides of an inequality by a negative number?
5. Can you explain how to graph the solution \( y > -3 \) on a number line?
6. How do you check if a solution to an inequality is correct?
7. What is the difference between solving an equation and an inequality?
8. How can inequalities be used to describe real-world situations?

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

Learn how to solve the inequality 5y + 6y - 81 < 7y + 102 + 65y step-by-step with a detailed explanation. This problem involves combining like terms and solving linear inequalities. Suitable for students in Grades 7-9.

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