To solve the inequality \(5|y + 3| < 15\), follow these steps:

1. **Isolate the absolute value expression:**

   Divide both sides by 5 to get:
   \[
   |y + 3| < \frac{15}{5}
   \]
   Simplify the right side:
   \[
   |y + 3| < 3
   \]

2. **Set up the compound inequality:**

   Since \(|y + 3| < 3\), this implies:
   \[
   -3 < y + 3 < 3
   \]

3. **Solve the compound inequality:**

   Subtract 3 from all parts of the inequality:
   \[
   -3 - 3 < y + 3 - 3 < 3 - 3
   \]
   Simplify:
   \[
   -6 < y < 0
   \]

So, the solution to the inequality is:
\[
y \in (-6, 0)
\]

This means that \(y\) must be between \(-6\) and \(0\), but not including \(-6\) or \(0\).

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Would you like to go deeper into any of these steps? Here are some related questions:

1. How do you solve absolute value inequalities that involve a "greater than" sign?
2. What if the inequality was \(5|y + 3| \leq 15\)?
3. How would the solution change if the inequality was \(5|y + 3| > 15\)?
4. Can absolute value inequalities result in no solution? If so, when?
5. What is the geometric interpretation of absolute value inequalities?

**Tip:** When solving absolute value inequalities, remember that \( |x| < a \) implies \( -a < x < a \), and \( |x| > a \) implies \( x < -a \) or \( x > a \).

Learn how to solve the absolute value inequality 5|y + 3| < 15 with a detailed step-by-step solution. This problem covers key algebraic concepts including absolute value inequalities and their solutions. Suitable for high school students.

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