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Let's tackle the problems shown in the image one by one:

### 3) Solve the inequality, graph the answers, and write in interval notation:
You have two inequalities to solve here:

1. \( 8h - 2 < -10 \)
2. \( -h + 1 \leq -2 \)
3. \( -5 \leq 2x - 7 < 9 \)

Let's start solving each inequality:

#### a) \( 8h - 2 < -10 \)
1. Add 2 to both sides:
   \[
   8h < -8
   \]
2. Divide by 8:
   \[
   h < -1
   \]

#### b) \( -h + 1 \leq -2 \)
1. Subtract 1 from both sides:
   \[
   -h \leq -3
   \]
2. Multiply by \(-1\) (and flip the inequality sign):
   \[
   h \geq 3
   \]

#### c) \( -5 \leq 2x - 7 < 9 \)
1. Add 7 to all parts:
   \[
   2 \leq 2x < 16
   \]
2. Divide by 2:
   \[
   1 \leq x < 8
   \]

### Interval Notation:
Now, let's write the solutions in interval notation.

1. For \( h < -1 \), the solution is \( (-\infty, -1) \).
2. For \( h \geq 3 \), the solution is \( [3, \infty) \).
3. For \( 1 \leq x < 8 \), the solution is \( [1, 8) \).

### 4) What is the difference between rational numbers and integers?
- **Rational numbers** include all numbers that can be expressed as a fraction \(\frac{a}{b}\), where \(a\) and \(b\) are integers, and \(b \neq 0\). This includes fractions, terminating, and repeating decimals.
- **Integers** are whole numbers, including negatives, zero, and positives, i.e., \( \{ \dots, -2, -1, 0, 1, 2, \dots \} \). Every integer is a rational number, but not every rational number is an integer.

### 5) What is the difference between integers and the whole number set?
- **Integers** include all positive and negative whole numbers and zero, i.e., \( \{ \dots, -2, -1, 0, 1, 2, \dots \} \).
- **Whole numbers** include all non-negative integers, i.e., \( \{ 0, 1, 2, 3, \dots \} \).

Would you like details or have any questions on these solutions?

Here are five related questions for further understanding:
1. How do you graph the solution for the inequality \(h < -1\) and \(h \geq 3\) on a number line?
2. What are some examples of rational numbers that are not integers?
3. How can you determine if a given number is an integer or not?
4. What is the union of the solution sets for the inequalities \( h < -1 \) and \( h \geq 3 \)?
5. What are the key properties that distinguish whole numbers from natural numbers?

**Tip**: When solving inequalities with negative coefficients, always remember to flip the inequality sign when multiplying or dividing by a negative number.

Solve the inequality, graph the answers, and write in interval notation: 8h - 2 < -10 or -h + 1 ≤ -2. Also, what is the difference between rational numbers and integers, and what is the difference between integers and the whole number set?

This problem covers how to solve inequalities like 8h - 2 < -10 and understand key differences between rational numbers, integers, and whole numbers. Step-by-step solution and graphing tips provided, suitable for students in Grades 8-10.

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