3. Graph the inequality -4 < x < -1 on the number line below and express in interval notation. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 67 4. Graph the interval (-∞, 2] below: -7-6-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 5. Solve the following inequality and express your answer in interval notation: -3r+4>-8 -7-6-5-4-3 -2 -1 0 1 2 3 - 4 5 67 @
3. Graph the inequality -4 < x < -1 on the number line below and express in interval notation. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 67 4. Graph the interval (-∞, 2] below: -7-6-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 5. Solve the following inequality and express your answer in interval notation: -3r+4>-8 -7-6-5-4-3 -2 -1 0 1 2 3 - 4 5 67 @
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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I don’t know if I did all correct but I need help
![### Understanding Inequalities and Intervals
#### 3. Graph the Inequality -4 < x ≤ -1
To graph the inequality \(-4 < x \leq -1\) on a number line:
**Explanation:**
- A number line ranging from -7 to 7 is depicted.
- An open circle (indicating that -4 is not included) is placed at -4.
- A closed circle (indicating that -1 is included) is placed at -1.
- A dark, continuous thick line connects the two circles between -4 and -1, representing all the values x can take.
**Interval Notation:** The solution in interval notation is \((-4, -1]\).
#### 4. Graph the Interval \((-∞, 2]\)
To graph the interval \((-∞, 2]\) on a number line:
**Explanation:**
- A number line ranging from -7 to 7 is depicted.
- The graph includes all numbers from negative infinity up to, and including, 2.
- This is represented by a dark continuous line starting from the left towards 2, with a closed circle at 2 (indicating that 2 is included).
**Interval Notation:** The interval in notation form is \((-∞, 2]\).
#### 5. Solve the Inequality and Express in Interval Notation: \(-3x + 4 \geq -8\)
**Steps to Solve:**
1. Start with the inequality:
\[
-3x + 4 \geq -8
\]
2. Subtract 4 from both sides:
\[
-3x \geq -12
\]
3. Divide by -3 (note that dividing by a negative number reverses the inequality sign):
\[
x \leq 4
\]
**Graphing:**
**Explanation:**
- A number line ranging from -7 to 7 is depicted.
- The graph includes all numbers less than and equal to 4.
- This is represented by a dark continuous line starting from the left towards 4, with a closed circle at 4 (indicating that 4 is included).
**Interval Notation:** In interval notation, this can be written as \((-\infty, 4]\).
Understanding these graphs and notations is crucial for visualizing and comprehending the range](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d3dbcbf-1187-4851-b302-b7975eeafa56%2F9cf8056f-382d-4442-8842-7333021d7b37%2F30hsh6s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Inequalities and Intervals
#### 3. Graph the Inequality -4 < x ≤ -1
To graph the inequality \(-4 < x \leq -1\) on a number line:
**Explanation:**
- A number line ranging from -7 to 7 is depicted.
- An open circle (indicating that -4 is not included) is placed at -4.
- A closed circle (indicating that -1 is included) is placed at -1.
- A dark, continuous thick line connects the two circles between -4 and -1, representing all the values x can take.
**Interval Notation:** The solution in interval notation is \((-4, -1]\).
#### 4. Graph the Interval \((-∞, 2]\)
To graph the interval \((-∞, 2]\) on a number line:
**Explanation:**
- A number line ranging from -7 to 7 is depicted.
- The graph includes all numbers from negative infinity up to, and including, 2.
- This is represented by a dark continuous line starting from the left towards 2, with a closed circle at 2 (indicating that 2 is included).
**Interval Notation:** The interval in notation form is \((-∞, 2]\).
#### 5. Solve the Inequality and Express in Interval Notation: \(-3x + 4 \geq -8\)
**Steps to Solve:**
1. Start with the inequality:
\[
-3x + 4 \geq -8
\]
2. Subtract 4 from both sides:
\[
-3x \geq -12
\]
3. Divide by -3 (note that dividing by a negative number reverses the inequality sign):
\[
x \leq 4
\]
**Graphing:**
**Explanation:**
- A number line ranging from -7 to 7 is depicted.
- The graph includes all numbers less than and equal to 4.
- This is represented by a dark continuous line starting from the left towards 4, with a closed circle at 4 (indicating that 4 is included).
**Interval Notation:** In interval notation, this can be written as \((-\infty, 4]\).
Understanding these graphs and notations is crucial for visualizing and comprehending the range
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