Question

complete problems 3-5.
3 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.
b. how would you write the opposite of 7?
c. +12 means ______.
d. what are two ways to write positive 9?
5 ethan is playing a video game. on each turn, he can earn positive points, negative points, or zero points. he starts with zero points.
a. after the first round, ethan has -150 points. label the tick marks and place a point at -150.
b. next to each description, write one of these numbers: -100, 50, 0.
a score greater than 0: ______
a score at the start of the game: ______
a score less than 0: ______
c. what is the opposite of -150? where is this value on the number line? explain how you know.
vocabulary
opposite numbe
numbers that are
the same distance
from 0 on the num
line but in opposi
directions. oppos
numbers have th
same numeral, b
opposite sign

Explanation:

Problem 3

Part a

Step1: Recall distance on number line

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

Step1: Analyze position relative to 0

Positive numbers are above (to the right) of 0 on the number line. 4 is positive, so it is above 0.

Step1: Define opposite of a number

The opposite of a number \( a \) is \( -a \) (or \( a \) is the opposite of \( -a \)), and they are equidistant from 0. For 4, the opposite is \( - 4 \). To plot it, find the point 4 units below (to the left) of 0 on the number line, same distance from 0 as 4.

Answer:

4 units

Part b