https://file.aiquickdraw.com/mathbot/file/1728255967278gd9ago4n.jpg

The system of linear inequalities given is:

\[
-2 \leq x < 3
\]

This inequality represents all values of \( x \) that are between \(-2\) and \(3\), including \(-2\) but not including \(3\). To graph this on a number line:

1. Place a **closed circle** at \(-2\) to indicate that \(-2\) is included in the solution set.
2. Place an **open circle** at \(3\) to indicate that \(3\) is not included in the solution set.
3. Shade the region between \(-2\) and \(3\) to show all the values \( x \) that satisfy the inequality.

This visually demonstrates that any \( x \) in the interval \([-2, 3)\) is a solution.

Would you like further details or have any questions?

Here are 5 related questions to expand on this information:
1. How would the graph change if the inequality were \( -2 < x \leq 3 \)?
2. What is the difference between an open and a closed circle on a number line?
3. How would you write the interval notation for this solution set?
4. How can this inequality be represented on a coordinate plane instead of a number line?
5. What would the graph look like if the inequality were \( x > -2 \) and \( x \leq 3 \)?

**Tip:** When graphing inequalities, remember that a closed circle means the endpoint is included (≤ or ≥), while an open circle means it is not included (< or >).

Graph the solution of the system of linear inequalities: -2 ≤ x < 3

Learn how to graph the linear inequality -2 ≤ x < 3 on a number line. This lesson covers important concepts related to inequalities, including closed and open circles, and visualizing solutions between -2 and 3. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation