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5. Complete the table below. Inequality x < 0 -00 -2

5. Complete the table below. Inequality x < 0 -00 -2

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Understanding Inequalities and Their Graphical Representations In mathematics, inequalities are used to describe the relative size or order of two objects. This table demonstrates how to translate between inequality statements, their graphical representations on a number line, and their corresponding interval notations. #### Table: Inequalities, Graphs, and Interval Notations | **Inequality** | **Graph** | **Interval Notation** | |----------------|-----------|-----------------------| | \( x < 0 \) | ![Graph](https://example.com/X-less-than-0.png) | \( (-\infty, 0) \) | | \( -2 < x \leq 1 \) | ![Graph](https://example.com/Between-negative-2-and-1.png) | \( (-2, 1] \) | | \( x \geq -3 \) | ![Graph](https://example.com/Greater-than-or-equal-negative-3.png) | \( [-3, \infty) \) | #### Graphical Explanation 1. **Graph for \( x < 0 \)**: - The number line starts from negative infinity to positive infinity. - The portion of the line to the left of 0 is highlighted. - An open circle at 0 indicates that 0 is not included in the range, which corresponds to the inequality \( x < 0 \). - **Interval Notation**: \( (-\infty, 0) \) 2. **Graph for \( -2 < x \leq 1 \)**: - The number line shows a segment starting after -2 and including 1. - An open circle at -2 indicates that -2 is not included, while a closed circle at 1 shows 1 is included. - **Interval Notation**: \( (-2, 1] \) 3. **Graph for \( x \geq -3 \)**: - The number line highlights the portion from -3 extending to positive infinity. - A closed circle at -3 indicates that -3 is included in the range. - **Interval Notation**: \( [-3, \infty) \) Understanding the correspondence between inequalities, number line graphs, and interval notations can help in visualizing and solving inequalities more effectively in algebra.
Transcribed Image Text:### Understanding Inequalities and Their Graphical Representations In mathematics, inequalities are used to describe the relative size or order of two objects. This table demonstrates how to translate between inequality statements, their graphical representations on a number line, and their corresponding interval notations. #### Table: Inequalities, Graphs, and Interval Notations | **Inequality** | **Graph** | **Interval Notation** | |----------------|-----------|-----------------------| | \( x < 0 \) | ![Graph](https://example.com/X-less-than-0.png) | \( (-\infty, 0) \) | | \( -2 < x \leq 1 \) | ![Graph](https://example.com/Between-negative-2-and-1.png) | \( (-2, 1] \) | | \( x \geq -3 \) | ![Graph](https://example.com/Greater-than-or-equal-negative-3.png) | \( [-3, \infty) \) | #### Graphical Explanation 1. **Graph for \( x < 0 \)**: - The number line starts from negative infinity to positive infinity. - The portion of the line to the left of 0 is highlighted. - An open circle at 0 indicates that 0 is not included in the range, which corresponds to the inequality \( x < 0 \). - **Interval Notation**: \( (-\infty, 0) \) 2. **Graph for \( -2 < x \leq 1 \)**: - The number line shows a segment starting after -2 and including 1. - An open circle at -2 indicates that -2 is not included, while a closed circle at 1 shows 1 is included. - **Interval Notation**: \( (-2, 1] \) 3. **Graph for \( x \geq -3 \)**: - The number line highlights the portion from -3 extending to positive infinity. - A closed circle at -3 indicates that -3 is included in the range. - **Interval Notation**: \( [-3, \infty) \) Understanding the correspondence between inequalities, number line graphs, and interval notations can help in visualizing and solving inequalities more effectively in algebra.
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