Draw a number line to represent the following real numbers: a) x <= -1 or x >= 1/2, b) −6 < x and x <= -2. Use a number line to determine the distance between -3 and 2. Represent 0.2 on a number line.

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Question 8: Draw a number line to present each of the real numbers.

• a) $x \le -1$ or $x \ge \frac{1}{2}$ Draw a number line. Place a solid dot at -1 and draw a thick line extending from this dot to the left (towards negative infinity). Place a solid dot at $\frac{1}{2}$ (or 0.5) and draw a thick line extending from this dot to the right (towards positive infinity).

• b) $-6 < x$ and $x \le -2$ (This can be written as $-6 < x \le -2$) Draw a number line. Place an open circle at -6. Place a solid dot at -2. Draw a thick line segment connecting the open circle at -6 and the solid dot at -2.

Question 9: Use a number line to determine the distance between:

• a) -3 and 2 To find the distance between two points on a number line, you can subtract the smaller number from the larger number, or use the absolute value of their difference. Distance $= |2 - (-3)| = |2 + 3| = |5| = 5$. On a number line, mark -3 and 2. Count the units between them: from -3 to -2 (1 unit), to -1 (2 units), to 0 (3 units), to 1 (4 units), to 2 (5 units). The distance is $\boxed{\text{5 units}}$.

Question 10: Represent the given set of real numbers on a number line.

• a) 0.2 Draw a number line. Place a solid dot at the position corresponding to 0.2 (which is between 0 and 1, closer to 0).

• b) 0.4 Draw a number line. Place a solid dot at the position corresponding to 0.4 (which is between 0 and 1, slightly less than halfway).

• c) 0.6 Draw a number line. Place a solid dot at the position corresponding to 0.6 (which is between 0 and 1, slightly more than halfway).