"And" inequalities are true when the inequalities overlap.For example, if the solution to an inequality is `x>4` and `x<7`, which of the following images correctly represent this?A)B)C)D) ### Understanding Inequality Notation on Number LinesThe image contains four number lines (A, B, C, D) each demonstrating different ways to represent inequalities on a number line. Detailed explanations of each number line are provided below:#### Number Line A- An arrow extends indefinitely to both the left and right, indicating that the line continues towards negative and positive infinity, respectively.- Whole numbers from -1 through 7 are marked on the line.- Circles are drawn around the numbers 4 and 7.- This representation shows that the inequality involves all numbers between 4 and 7, including 4 but not including 7 (notation: $ 4 \leq x < 7 $).#### Number Line B- Similar to Number Line A, an arrow points in both the left and right directions.- Whole numbers from -1 through 7 are indicated.- Circles are marked around the numbers 4 and 7.- The arrow pointing to the right starts from 7. - This represents numbers greater than or equal to 7 in the inequality, while 4 is also included (notation: $ 4 \leq x \leq 7 $ or $ 4 \leq x \leq \infty $).#### Number Line C- Arrows extend to both left and right, indicating continuity towards negative and positive infinity.- Whole numbers from -1 through 7 are labeled.- A circle surrounds the number 4, and another surrounds the number 7.- The arrow pointing to the left starts from -1.- This indicates all numbers less than 4 and all numbers equal to 7 (notation: $ x < 4 $ or $ x = 7 $).#### Number Line D- An arrow points infinitely to the right only, suggesting the line extends towards positive infinity.- All whole numbers from -1 through 7 are labeled.- A circle surrounds the number 7.- This represents all numbers less than or equal to 7 (notation: $ x \leq 7 $).By understanding these graphical representations on number lines, students can effectively visualize and interpret inequalities in mathematics.

First, we plot x>4 Here anyhting on the right side of 4 is included in the shaded region

Answered: And" inequalities are true when the…

And" inequalities are true when the inequalities overlap. For example, if the solution to an inequality is `x>4` and `x<7`, which of the following images correctly represent this? A) B) C) D)

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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"And" inequalities are true when the inequalities overlap.

For example, if the solution to an inequality is `x>4` and `x<7`, which of the following images correctly represent this?

### Understanding Inequality Notation on Number Lines

The image contains four number lines (A, B, C, D) each demonstrating different ways to represent inequalities on a number line. Detailed explanations of each number line are provided below:

#### Number Line A
- An arrow extends indefinitely to both the left and right, indicating that the line continues towards negative and positive infinity, respectively.
- Whole numbers from -1 through 7 are marked on the line.
- Circles are drawn around the numbers 4 and 7.
- This representation shows that the inequality involves all numbers between 4 and 7, including 4 but not including 7 (notation: $ 4 \leq x < 7 $).

#### Number Line B
- Similar to Number Line A, an arrow points in both the left and right directions.
- Whole numbers from -1 through 7 are indicated.
- Circles are marked around the numbers 4 and 7.
- The arrow pointing to the right starts from 7.
- This represents numbers greater than or equal to 7 in the inequality, while 4 is also included (notation: $ 4 \leq x \leq 7 $ or $ 4 \leq x \leq \infty $).

#### Number Line C
- Arrows extend to both left and right, indicating continuity towards negative and positive infinity.
- Whole numbers from -1 through 7 are labeled.
- A circle surrounds the number 4, and another surrounds the number 7.
- The arrow pointing to the left starts from -1.
- This indicates all numbers less than 4 and all numbers equal to 7 (notation: $ x < 4 $ or $ x = 7 $).

#### Number Line D
- An arrow points infinitely to the right only, suggesting the line extends towards positive infinity.
- All whole numbers from -1 through 7 are labeled.
- A circle surrounds the number 7.
- This represents all numbers less than or equal to 7 (notation: $ x \leq 7 $).

By understanding these graphical representations on number lines, students can effectively visualize and interpret inequalities in mathematics.

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