https://r2.erweima.ai/mathbot/image/1726518211087ug4ahas2.jpg

Let's go through the questions one by one:

### 9. Question: **Which city has the greatest difference between day and night temperatures?**
- **Table of cities:**
  - **İzmir**: Night +6°C, Day +16°C → Difference = 16°C - 6°C = 10°C
  - **Erzurum**: Night -16°C, Day -8°C → Difference = -8°C - (-16°C) = 8°C
  - **Denizli**: Night 0°C, Day +2°C → Difference = 2°C - 0°C = 2°C
  - **Ankara**: Night -10°C, Day -2°C → Difference = -2°C - (-10°C) = 8°C

The greatest difference is in **İzmir** (10°C). The answer is **A) İzmir**.

---

### 10. Question: **What is the maximum difference between two three-digit even numbers with different digits?**
- Maximum three-digit even number = 986
- Minimum three-digit even number = 102
- Difference = 986 - 102 = **884**

The answer is **D) 2000** is incorrect, but should be **C) 1974**, assuming you wanted maximum difference.

---

### 11. Question: **Find the incorrect equation based on the number line.**
Given that the number line divides the distance between points \( A \) and \( B \) into equal segments, we need to evaluate the given options.

- A) \( x + t = 0 \)
- B) \( z - y = 2 \)
- C) \( x - z = -14 \)
- D) \( t - y = 12 \)

The incorrect one appears to be **C) x - z = -14**, since the position of \( x \) and \( z \) seems not to match that relation.

---

### 12. Question: **Find the result of \( | -15 | - | -20 | + | 1 | \).**

- \( | -15 | = 15 \)
- \( | -20 | = 20 \)
- \( | 1 | = 1 \)

The operation becomes:
\[ 15 - 20 + 1 = -4 \]

The answer is **D) -4**.

---

### 13. Question: **Calculate \( A = | -11 - |6| | \) and \( B = | 16 - | -14 | | \), then find \( A - B \).**

- \( A = | -11 - |6| | = | -11 - 6 | = | -17 | = 17 \)
- \( B = | 16 - | -14 | | = | 16 - 14 | = | 2 | = 2 \)
- \( A - B = 17 - 2 = 15 \)

The answer is **A) 15**.

---

### 14. Question: **Simplify \( | 9 - 8 | - | 1 - 4 | + | 9 - 2 + 1 | \).**

- \( | 9 - 8 | = 1 \)
- \( | 1 - 4 | = 3 \)
- \( | 9 - 2 + 1 | = | 8 | = 8 \)

The operation becomes:
\[ 1 - 3 + 8 = 6 \]

The answer is **D) 6**.

---

### 15. Question: **Choose the correct visual representation for \( 0 - (-3) \).**

Subtracting a negative is equivalent to adding a positive, so the answer should depict \( 0 + 3 \), which means **adding three positive counters**. The correct model is **B)**.

---

If you would like further clarifications on any of these, feel free to ask!

### Related Questions:
1. How would the solution change if the temperature values were negative for all cities?
2. What is the formula for absolute value and how is it applied in algebraic problems?
3. Can you explain in more detail how to break down large subtractions into smaller steps for clarity?
4. What strategies can be used to simplify complex number line problems?
5. How does modeling subtraction with counters help understand negative numbers?

### Tip:
When solving problems with absolute values, simplify the inner expressions first before applying the absolute value operation.

The original question submitted by the user as text.

Detailed solutions to problems involving absolute value, temperature differences, even numbers, and number lines. Topics include solving equations with absolute value and representing operations with visuals. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation