Question

complete problems 3–5. look at the point at 4 on the number line. a. how many units is 4 from 0? b. is 4 located above or below 0? c. plot a point at the opposite of 4 on the number line. explain how you know it is the opposite. 4. a. −10 means the opposite of ____ or ____ 10.

Explanation:

Part a

Step1: Recall distance on number line

The distance between a number \( x \) and \( 0 \) on the number line is given by \( |x - 0|=|x| \).
For \( x = 4 \), we calculate \( |4| \).

Step2: Evaluate the absolute value

The absolute value of a non - negative number \( a \) is \( a \) itself. Since \( 4\geq0 \), \( |4| = 4 \).

Step1: Recall number line positions

On the number line, positive numbers are located to the right (above, in a vertical sense of number line representation) of \( 0 \), and negative numbers are located to the left (below) of \( 0 \).

Step2: Determine the position of 4

Since \( 4\) is a positive number, it is located above \( 0 \) on the number line.

Step1: Find the opposite of 4

The opposite of a number \( a \) is \( -a \). So, the opposite of \( 4 \) is \( - 4 \).

Step2: Plot the point

On the given number line, we look for the position of \( - 4 \). The number line has marks at \( - 5,-4,-3,-2,-1,0,1,2,3,4,5 \). We plot the point at the mark labeled \( - 4 \). To know it's the opposite, we use the definition: two numbers are opposites if they are the same distance from \( 0 \) but on opposite sides of \( 0 \). The distance of \( 4 \) from \( 0 \) is \( |4| = 4 \) units, and the distance of \( - 4 \) from \( 0 \) is \( |-4|=4 \) units, and \( 4 \) is to the right of \( 0 \) while \( - 4 \) is to the left of \( 0 \).

Answer:

4

Part b