https://file.aiquickdraw.com/mathbot/file/1727033893478omx4gjdd.jpg

The given problem shows a compound inequality, with one part involving \( y \leq \frac{-11}{3} \) and the other involving \( y > -3 \). The solution asks for the interval notation for the combined inequality.

### Understanding the Compound Inequality:
We have:
1. \( y \leq \frac{-11}{3} \)
2. \( y > -3 \)

These two inequalities need to be combined. From the image, it is unclear if we are dealing with a union (\( \cup \)) or an intersection (\( \cap \)) of these inequalities. Let’s explore both cases:

1. **Intersection (\( \cap \))**: 
   The solution would involve numbers that satisfy both inequalities simultaneously. This requires the values of \( y \) to be greater than \( -3 \) and less than or equal to \( \frac{-11}{3} \).
   \[
   -3 < y \leq \frac{-11}{3}
   \]
   In interval notation, this is:
   \[
   (-3, \frac{-11}{3}]
   \]

2. **Union (\( \cup \))**: 
   If instead the union is meant, the solution would include all numbers that satisfy either inequality:
   \[
   y \in (-\infty, \frac{-11}{3}] \cup (-3, \infty)
   \]
   But this doesn't seem to apply here, because it would cover the entire real line without clear constraints.

Given the layout, the expected solution is likely **intersection**, so the answer in **interval notation** would be:
\[
(-3, \frac{-11}{3}]
\]

Would you like further details or clarifications on this? Here are some related questions to explore:

1. How do you graphically represent compound inequalities?
2. What is the difference between union and intersection in set theory?
3. How do we convert inequalities into interval notation?
4. Why is it important to use open or closed intervals in notation?
5. What happens if the inequality signs change?

**Tip**: Always pay attention to whether the problem specifies the use of an intersection or union in compound inequalities. This dramatically changes the solution set.

Thus, the solution set is | y ≤ -11/3 or y > -3. The solution set in interval notation is?

Learn how to solve the compound inequality y ≤ -11/3 and y > -3. This step-by-step guide explains how to combine inequalities and express the solution in interval notation. Suitable for Grades 8-10 students learning inequalities.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation