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To solve the inequality \( 5y + 9 \leq 4 \):

1. **Subtract 9 from both sides** of the inequality to isolate the term with \( y \) on one side:
   \[
   5y + 9 - 9 \leq 4 - 9
   \]
   This simplifies to:
   \[
   5y \leq -5
   \]

2. **Divide both sides by 5** to solve for \( y \):
   \[
   y \leq \frac{-5}{5}
   \]
   Simplifying this gives:
   \[
   y \leq -1
   \]

So the solution to the inequality is \( y \leq -1 \).

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

Here are five related questions to further explore this topic:
1. How would you graph the solution \( y \leq -1 \) on a number line?
2. How does the solution change if the inequality were \( 5y + 9 \geq 4 \) instead?
3. What would happen if the inequality were \( 5y + 9 < 4 \) instead of \( \leq \)?
4. How do you solve an inequality that involves division by a negative number?
5. How can you verify the solution to an inequality?

**Tip:** When solving inequalities, if you multiply or divide both sides by a negative number, remember to reverse the inequality sign.

Learn how to solve the linear inequality 5y + 9 ≤ 4 with a clear, step-by-step solution. This problem covers key algebraic concepts such as isolating variables and understanding the properties of inequalities, making it suitable for students in Grades 7-9.

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