epresent the following sets on a nur a) $$ \{x: x \leq 7 ; x \in \mathbb{Z}\} $$

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To represent the set $$ \{x: x \leq 7 ; x \in \mathbb{Z}\} $$ on a **number line**, we'll depict all integer values that are less than or equal to 7. Here's how you can visualize it:

### Set Description:
- **Set:** $$ \{x: x \leq 7 ; x \in \mathbb{Z}\} $$
- **Elements:** All integers (ℤ) that are less than or equal to 7.

### Number Line Representation:

```
<---●----●----●----●----●----●----●----●----●----●----●
    ...   3     4     5     6     7
```

### Explanation:

1. **Arrow to the Left (`<---`):**
   - Indicates that the set extends infinitely to the left, including all integers less than 7.

2. **Dots (`●`):**
   - Each filled dot represents an integer in the set.
   - Starting from 7 and moving to the left: 7, 6, 5, 4, 3, ..., continuing indefinitely.

3. **Numbers:**
   - The numbers below the dots label the integer values.
   - Only a portion of the number line is shown for clarity, but it extends infinitely to the left.

4. **Inclusion of 7:**
   - The dot at 7 is included, indicating that 7 is part of the set ($$ x \leq 7 $$).

### Visual Enhancement (Detailed):

For a clearer and more detailed representation, consider the following expanded number line:

```
<---|----|----|----|----|----|----|----|----|----|----|-->
   ...   -2    -1     0     1     2     3     4     5     6     7
                                      ●     ●     ●     ●     ●
```

- **Filled Dots (`●`):** Indicate that each corresponding integer is included in the set.
- **Empty Spaces:** Represent numbers not shown but are part of the infinite extension to the left.

### Summary:

- **All integers** less than or equal to 7 are included.
- **Representation** is shown using filled dots on the number line up to 7, with an arrow indicating the continuation of integers indefinitely to the left.

Feel free to redraw this number line on paper or using graphic software for a more precise visual representation!
All integers less than or equal to 7 are represented on the number line with filled dots up to 7, extending infinitely to the left.

epresent the following sets on a nur a) \( \{x: x \leq 7 ; x \in \mathbb{Z}\} \)

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