Question

1. mark the number line to show how you would find or illustrate | - 4 | and | 3 |.
2. put the correct sign between each pair of numbers: >, ≥, <, ≤, =

a. \\(\frac{3}{4}\\) \\(\square\\) -2
b. 5 \\(\square\\) \\(\frac{10}{2}\\)
c. -1 \\(\square\\) 0
d. -3 \\(\square\\) -1

Explanation:

Problem 6

Step1: Recall absolute value definition

The absolute value of a number \( x \), denoted \( |x| \), is the distance of \( x \) from 0 on the number line. So \( | - 4| \) is the distance from -4 to 0, and \( |3| \) is the distance from 3 to 0.

Step2: Find \( | - 4| \)

The distance from -4 to 0 is 4 units (since we move 4 units to the right from -4 to 0). So \( | - 4|=4 \). On the number line, we mark 4 (which is the same as +4) to represent \( | - 4| \).

Step3: Find \( |3| \)

The distance from 3 to 0 is 3 units (we move 3 units to the left from 3 to 0). So \( |3| = 3\). On the number line, we mark +3 to represent \( |3| \).

Step1: Recall number types

\( \frac{3}{4} \) is a positive fraction (greater than 0), and -2 is a negative integer (less than 0).

Step2: Compare positive and negative

Positive numbers are always greater than negative numbers. So \( \frac{3}{4}> - 2 \).

Step1: Simplify \( \frac{10}{2} \)

Simplify the fraction \( \frac{10}{2} \) by dividing 10 by 2. \( \frac{10}{2}=5 \).

Step2: Compare 5 and 5

Since both numbers are equal (5 = 5), we use the equal sign.

Answer:

To illustrate \( | - 4| \), mark the point at \( + 4 \) (since \( | - 4|=4 \)) on the number line. To illustrate \( |3| \), mark the point at \( + 3 \) (since \( |3| = 3\)) on the number line.

Problem 7

Part (a)