Please do step by step so i can be able to understand? **Title: Solving and Graphing Inequalities**---**Problem Statement:**Solve and write interval notation for the solution set. Then graph the solution set.Given Inequality:\[ 3 \leq x - 2 \leq 6 \]---**Instructions:**Select the correct choice below and fill in any answer boxes in your choice.**Options:**- **A.** The solution set is [ _ ]. *(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)*- **B.** There is no solution.Choose the correct graph of the solution.---**Graphs:**1. **Option A (Graph):** - The number line ranges from 0 to 12. - The section from negative infinity to 4 is shaded to the left (including negative infinity). ![Diagram A](graph_A)2. **Option B (Graph):** - The number line ranges from 0 to 12. - The section from 5 (inclusive) to 9 (inclusive) is shaded. ![Diagram B](graph_B)3. **Option C (Graph):** - The number line ranges from 0 to 12. - The section from 5 (inclusive) to 8 (inclusive) is shaded. ![Diagram C](graph_C)4. **Option D (Graph):** - The number line ranges from 0 to 12. - The sections from 5 to 6 (inclusive) and 7 to 8 (inclusive) are shaded. ![Diagram D](graph_D)5. **Option E (Graph):** - The number line ranges from 0 to 12. - The section from 2 to infinity is shaded to the right. ![Diagram E](graph_E)6. **Option F (Graph):** - The number line ranges from 0 to 12. - The section from negative infinity to 4 is shaded to the left (including negative infinity). ![Diagram F](graph_F)---**Solution:**The inequality can be simplified as follows:- Original Inequality: \(3 \leq x - 2 \leq 6\)- Add 2 to all parts: \(5 \leq x \leq 8\)

Answered: Solve and write interval notation for…

Math

Calculus

Solve and write interval notation for the solution set. Then graph the solution set.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Please do step by step so i can be able to understand?

**Title: Solving and Graphing Inequalities**

---

**Problem Statement:**
Solve and write interval notation for the solution set. Then graph the solution set.

Given Inequality:
\[ 3 \leq x - 2 \leq 6 \]

---

**Instructions:**
Select the correct choice below and fill in any answer boxes in your choice.

**Options:**
- **A.** The solution set is [ _ ].
*(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)*
- **B.** There is no solution.

Choose the correct graph of the solution.

---

**Graphs:**

1. **Option A (Graph):**
- The number line ranges from 0 to 12.
- The section from negative infinity to 4 is shaded to the left (including negative infinity).

![Diagram A](graph_A)

2. **Option B (Graph):**
- The number line ranges from 0 to 12.
- The section from 5 (inclusive) to 9 (inclusive) is shaded.

![Diagram B](graph_B)

3. **Option C (Graph):**
- The number line ranges from 0 to 12.
- The section from 5 (inclusive) to 8 (inclusive) is shaded.

![Diagram C](graph_C)

4. **Option D (Graph):**

- The number line ranges from 0 to 12.
- The sections from 5 to 6 (inclusive) and 7 to 8 (inclusive) are shaded.

![Diagram D](graph_D)

5. **Option E (Graph):**
- The number line ranges from 0 to 12.
- The section from 2 to infinity is shaded to the right.

![Diagram E](graph_E)

6. **Option F (Graph):**
- The number line ranges from 0 to 12.
- The section from negative infinity to 4 is shaded to the left (including negative infinity).

![Diagram F](graph_F)

---

**Solution:**

The inequality can be simplified as follows:
- Original Inequality: \(3 \leq x - 2 \leq 6\)
- Add 2 to all parts: \(5 \leq x \leq 8\)

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