Question

1. point c is 5 units from 0 on a number line. write two numbers that could each be the location of point c.

1. point d is 8 units from its opposite on a number line. write the numbers that point d and its opposite represent.

1. use the number line to complete parts (a) and (b).

a. plot point f at $-5$.
b. plot point g at $-(-5)$.
c. describe the relationship between point f and point g.

1. write the number and describe its relationship to 0 on a number line.

a. ten
b. the opposite of ten
c. the opposite of the opposite of ten

1. sasha says that $-(-25)$ is equal to $-25$. julie disagrees and says that $-(-25)$ is equal to 25. who is correct? explain.

Explanation:

Question 5

Step1: Recall number line distance

On a number line, the distance of a point \( x \) from 0 is \( |x| \). So if \( |x| = 5 \), then \( x = 5 \) or \( x = -5 \).

Step1: Define opposite of a number

Let the number be \( x \), its opposite is \( -x \). The distance between \( x \) and \( -x \) is \( |x - (-x)| = |2x| \).

Step2: Solve for x

Given \( |2x| = 8 \), then \( 2x = 8 \) or \( 2x = -8 \). Solving \( 2x = 8 \) gives \( x = 4 \), solving \( 2x = -8 \) gives \( x = -4 \). The opposite of 4 is -4 and vice versa.

Step1: Locate -5 on number line

On the given number line, find the position corresponding to -5 (as marked in the image, F is at -5).

Answer:

5 and -5

Question 6