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

Step 6: (continued from previous interaction) a) Evaluate -18 - 4(2-4) - 2b ÷ 12. Step 1: Simplify the expression inside the parentheses. 2 - 4 = -2 Step 2: Substitute the simplified value back into the expression and perform multiplication. -18 - 4(-2) - 2b ÷ 12 -18 + 8 - 2b ÷ 12 Step 3: Perform addition/subtraction from left to right for the constant terms. -10 - 2b ÷ 12 Step 4: Perform the division. -10 - (2b)/(12) Step 5: Simplify the fraction. -10 - (b)/(6) The simplified expression is -10 - (b)/(6). b) Identify irrational numbers from the following list of numbers: sqrt(25), 0.54, 1.7264, 27.1238..., (13)/(3), [3]5. Step 1: Analyze each number to determine if it is rational or irrational. • 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. • (13)/(3). This is a fraction of two integers, so it is a rational number. • [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. Step 2: List the irrational numbers. The irrational numbers from the list are 27.1238... and [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. Step 1: Identify the numbers that 8 is divisible by (factors of 8). The factors of 8 are 1, 2, 4, 8. Step 2: Identify the first three of these factors. The first three factors are 1, 2, 4. Step 3: Check if these numbers satisfy the condition X < 8. 1 < 8, 2 < 8, 4 < 8. All satisfy the condition. The numbers are 1, 2, 4. ii. 21 X 28 if X is a whole number. Step 1: Identify whole numbers. Whole numbers are 0, 1, 2, 3, .... Step 2: List the whole numbers that are greater than or equal to 21 and less than or equal to 28. The numbers are 21, 22, 23, 24, 25, 26, 27, 28. b) If a < d, then 6 + (-2a) 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) 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'. Step 1: Simplify the expressions on both sides of the box. Left side: 6 + (-2a) = 6 - 2a Right side: 3 + (-2a) = 3 - 2a Step 2: Compare the two simplified expressions. We need to compare 6 - 2a and 3 - 2a. Step 3: Subtract -2a from both sides of the comparison. 6 - 2a - (-2a) vs 3 - 2a - (-2a) 6 vs 3 Step 4: Determine the inequality sign. Since 6 is greater than 3, the inequality sign is >. So, 6 - 2a > 3 - 2a. The inequality sign to insert is >. 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 $p