### Number Line VisualizationsTo enhance understanding of set notation and intervals, draw a number line for each of the following cases:**a) $ x \in (-6, 2) $**This represents all real numbers $ x $ between -6 and 2, not including -6 and 2. On the number line, this is indicated by an interval starting just after -6 and ending just before 2.**b) $ \{ x \in R : x > 3 \} $**This represents all real numbers $ x $ that are greater than 3. On the number line, this starts just after 3 and extends infinitely to the right.**c) $ y \in Z \text{ and } [-3, 7) $**This represents all integers $ y $ within the closed interval from -3 to 7, not including 7. On the number line, this includes -3, -2, -1, 0, 1, 2, 3, 4, 5, and 6.**d) $ \{ x \in N : x \ge -2 \} $**This represents all natural numbers $ x $ (which are typically positive whole numbers starting from 1). Since the interval $ x \ge -2 $ refers to values greater than or equal to -2, but natural numbers start from 1, this interval does **not have valid natural numbers** because natural numbers do not include negative numbers or zero.**e) $ \{ x \in R : -4 < x \le 5 \} $**This represents all real numbers $ x $ which are greater than -4 and less than or equal to 5. On the number line, this starts just after -4 and ends at the value of 5 including 5.### Visualization ExplanationTo visualize each interval:1. **Identify the interval limits (both open and closed) on the number line.**2. **Use an open circle to indicate that a number is not included (for example, -6 in case a).**3. **Use a closed circle to indicate that a number is included (for example, 5 in case e).**4. **Shade the region between the circles to indicate all the numbers included in the interval (for example, between -6 and 2 in case

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Answered: Draw a number line for each of the…

Draw a number line for each of the following: a) хе(-6; 2) b) {x E R:x > 3} c) y EZ and [-3; 7) d) {x € N: x 2 -2} e) (x E R: -4 < x< 5}

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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Question

### Number Line Visualizations

To enhance understanding of set notation and intervals, draw a number line for each of the following cases:

**a) $ x \in (-6, 2) $**

This represents all real numbers $ x $ between -6 and 2, not including -6 and 2. On the number line, this is indicated by an interval starting just after -6 and ending just before 2.

**b) $ \{ x \in R : x > 3 \} $**

This represents all real numbers $ x $ that are greater than 3. On the number line, this starts just after 3 and extends infinitely to the right.

**c) $ y \in Z \text{ and } [-3, 7) $**

This represents all integers $ y $ within the closed interval from -3 to 7, not including 7. On the number line, this includes -3, -2, -1, 0, 1, 2, 3, 4, 5, and 6.

**d) $ \{ x \in N : x \ge -2 \} $**

This represents all natural numbers $ x $ (which are typically positive whole numbers starting from 1). Since the interval $ x \ge -2 $ refers to values greater than or equal to -2, but natural numbers start from 1, this interval does **not have valid natural numbers** because natural numbers do not include negative numbers or zero.

**e) $ \{ x \in R : -4 < x \le 5 \} $**

This represents all real numbers $ x $ which are greater than -4 and less than or equal to 5. On the number line, this starts just after -4 and ends at the value of 5 including 5.

### Visualization Explanation

To visualize each interval:

1. **Identify the interval limits (both open and closed) on the number line.**
2. **Use an open circle to indicate that a number is not included (for example, -6 in case a).**
3. **Use a closed circle to indicate that a number is included (for example, 5 in case e).**
4. **Shade the region between the circles to indicate all the numbers included in the interval (for example, between -6 and 2 in case

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