Represent the following graphically. Give the answer in interval notation (use the example as quideline). 2.3. $$ -1

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Solve the system of inequalities by following steps:
- step0: Solve for $$x$$:
  $$\left\{ \begin{array}{l}-1-1\x\leq 5\end{array}\right.$$
- step2: Find the intersection:
  $$-1-3\x<0\x\geq 0\x<4\end{array}\right.$$
- step2: Find the intersection:
  $$x \in \varnothing $$
Let's analyze and represent each of the given inequalities and conditions step by step, providing the answers in interval notation.

### 2.3. $$ -1 < x \leq 5, x \in \mathbb{Z} $$
This means $$ x $$ can take integer values greater than -1 and up to and including 5. The integers that satisfy this condition are:
- $$ 0, 1, 2, 3, 4, 5 $$

**Interval Notation:** 
$$
( -1, 5 ]
$$

### 2.5. $$ -3 \leq x < 4 $$ or $$ 4 \leq x < 6, x \in \mathbb{R} $$
This condition can be split into two parts:
1. $$ -3 \leq x < 4 $$
2. $$ 4 \leq x < 6 $$

The union of these intervals gives:
- From -3 to 4 (including -3 but not 4)
- From 4 to 6 (including 4 but not 6)

**Interval Notation:** 
$$
[-3, 4) \cup [4, 6)
$$

### 2.7. $$ -1 < x < 5 $$ and $$ 4 \leq x \leq 7, x \in \mathbb{R} $$
For this condition, we need to find the intersection of the two intervals:
1. $$ -1 < x < 5 $$
2. $$ 4 \leq x \leq 7 $$

The intersection is:
- The values of $$ x $$ that satisfy both conditions are from 4 to 5.

**Interval Notation:** 
$$
[4, 5)
$$

### 2.10. $$ -1 \leq x < 5 $$ or $$ 4 \leq x \leq 6, x \in \mathbb{Z} $$
This condition can be split into two parts:
1. $$ -1 \leq x < 5 $$ gives integers: $$ -1, 0, 1, 2, 3, 4 $$
2. $$ 4 \leq x \leq 6 $$ gives integers: $$ 4, 5, 6 $$

The union of these integers is:
- $$ -1, 0, 1, 2, 3, 4, 5, 6 $$

**Interval Notation:** 
$$
[-1, 5] \text{ (considering integers)}
$$

### 2.11. $$ 3 \leq x < 5 $$ and $$ 4 \leq x \leq 8, x \in \mathbb{N} $$
For this condition, we need to find the intersection of the two intervals:
1. $$ 3 \leq x < 5 $$ gives natural numbers: $$ 3, 4 $$
2. $$ 4 \leq x \leq 8 $$ gives natural numbers: $$ 4, 5, 6, 7, 8 $$

The intersection is:
- The only natural number that satisfies both conditions is $$ 4 $$.

**Interval Notation:** 
$$
\{4\} \text{ (as a set)}
$$

### 4.5. Present the following real numbers graphically: All the numbers between -3 and 0 as well as from 2 up to 4.
This condition can be split into two parts:
1. All numbers between -3 and 0: $$ (-3, 0) $$
2. All numbers from 2 up to 4: $$ [2, 4) $$

**Interval Notation:** 
$$
(-3, 0) \cup [2, 4)
$$

### Summary of Interval Notations:
- **2.3:** $$ (-1, 5] $$
- **2.5:** $$ [-3, 4) \cup [4, 6) $$
- **2.7:** $$ [4, 5) $$
- **2.10:** $$ [-1, 5] $$
- **2.11:** $$ \{4\} $$
- **4.5:** $$ (-3, 0) \cup [2, 4) $$
Here are the interval notations for each condition: 1. **2.3:** $$ (-1, 5] $$ 2. **2.5:** $$ [-3, 4) \cup [4, 6) $$ 3. **2.7:** $$ [4, 5) $$ 4. **2.10:** $$ [-1, 5] $$ 5. **2.11:** $$ \{4\} $$ 6. **4.5:** $$ (-3, 0) \cup [2, 4) $$

Represent the following graphically. Give the answer in
interval notation (use the example as quideline).
2.3.
2.5. or
and
2.10 or .
2.11 and .
4.5 Present the following real numbers graptrically
All the rumbers brtween - 3 aud 0 as well as
from 2 up to 4 . (as well as’ means union)

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Represent the following graphically. Give the answer in interval notation (use the example as quideline). 2.3. 2.5. or and 2.10 or . 2.11 and . 4.5 Present the following real numbers graptrically All the rumbers brtween - 3 aud 0 as well as from 2 up to 4 . (as well as’ means union)