List the numbers which satisfy each of the following conditions. i. x < 8 if x is the first three divisible numbers of 8. ii. 21 <= x <= 28 if x is a whole number

a) Evaluate $-18 - 4(2-4) - 2b \div 12$.

The simplified expression is $\boxed{-10 - \frac{b}{6}}$.

b) Identify irrational numbers from the following list of numbers: $\sqrt{25}, 0.54, 1.7264, 27.1238..., \frac{13}{3}, \sqrt[3]{5}$.

• $\sqrt{25} = 5$. This is an integer, so it is a rational number.
• 0.54. This is a terminating decimal, so it is a rational number.
• 1.7264. This is a terminating decimal, so it is a rational number.
• 27.1238.... The ellipsis indicates that the decimal continues indefinitely without a repeating pattern. This is a non-terminating, non-repeating decimal, so it is an irrational number.
• $\frac{13}{3}$. This is a fraction of two integers, so it is a rational number.
• $\sqrt[3]{5}$. The cube root of 5 is not an integer or a simple fraction. Its decimal representation is non-terminating and non-repeating. This is an irrational number.

The irrational numbers from the list are $\boxed{27.1238... \text{ and } \sqrt[3]{5}}$.

7. a) List the numbers which satisfy each of the following conditions: i. $X < 8$ if $X$ is the first three divisible numbers of 8.

The factors of 8 are $1, 2, 4, 8$.

The first three factors are $1, 2, 4$.

$1 < 8$, $2 < 8$, $4 < 8$. All satisfy the condition.
The numbers are $\boxed{1, 2, 4}$.

ii. $21 \le X \le 28$ if $X$ is a whole number.

Whole numbers are $0, 1, 2, 3, ...$.

The numbers are $\boxed{21, 22, 23, 24, 25, 26, 27, 28}$.

b) If $a < d$, then $6 + (-2a) \boxed{\phantom{X}} 3 + (-2b)$. Insert inequality sign ($<$ or $>$) in the box to make a statement true.
Assumption: There is a typo in the question, and the expression should be $6 + (-2a) \boxed{\phantom{X}} 3 + (-2a)$ to allow for a comparison based on the given information. If the 'b' is intentional, the question cannot be answered without a relationship between 'a' and 'b' or 'd'.

Left side: $6 + (-2a) = 6 - 2a$
Right side: $3 + (-2a) = 3 - 2a$

We need to compare $6 - 2a$ and $3 - 2a$.

$6 - 2a - (-2a)$ vs $3 - 2a - (-2a)$
6 vs 3

Since 6 is greater than 3, the inequality sign is $>$.
So, $6 - 2a > 3 - 2a$.
The inequality sign to insert is $\boxed{>}$.

8. Careful study the following figure and answer the questions that follows. i. The figure above represents the arrangement of number systems.

ii. Name the category of numbers represented by letter A to F.
A: Natural Numbers (or Counting Numbers)
B: Whole Numbers
C: Integers
D: Rational Numbers
E: Irrational Numbers
F: Real Numbers

iii. How can you differentiate the category of numbers labeled by letter D and those labeled by letter E?
Rational numbers (D) can be expressed as a fraction $\frac{p}{