Math Problem Statement

Rewrite the set J by listing its elements. Make sure to use the appropriate set notation: J = {x | x is an integer and -5 < x ≤ -1}.

Solution

The image you provided asks to rewrite the set JJ using set-builder notation. The set is described as:

J={xx is an integer and 5<x1}J = \{ x \mid x \text{ is an integer and } -5 < x \leq -1 \}

This set is composed of integers xx that satisfy the condition 5<x1-5 < x \leq -1, meaning xx is between -5 and -1, not including -5 but including -1.

In set-builder notation, this can be rewritten as:

J={xZ5<x1}J = \{ x \in \mathbb{Z} \mid -5 < x \leq -1 \}

Here:

  • xZx \in \mathbb{Z} means that xx is an integer.
  • 5<x1-5 < x \leq -1 defines the range for xx.

Would you like further clarification on set-builder notation or related topics?


Here are 5 questions to expand your understanding:

  1. What is the difference between set-builder notation and interval notation?
  2. How would you express this set using interval notation if it was over real numbers?
  3. Can you represent a set of non-integers using set-builder notation?
  4. What are the rules for determining when a number belongs to a set in set-builder notation?
  5. How does the notation change if the set includes decimal or rational numbers?

Tip: Always pay attention to whether a set includes or excludes boundary points, such as using strict inequalities << or >>, versus \leq or \geq.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Set-Builder Notation
Inequalities

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9