If an integer a is pictured on the number line then the distance
from the point on the number line that represents the integer to the origin is ƒaƒ.
Using this idea answer the
following.
a. Explain why ƒa 2 bƒ is the distance between the points that represent the integers a and b.
b. One way to define “less than” for integers is as follows: a , b if and only if a is to the left of b on the number line.
Consequently b . a if and only if b is to the right of a.
Use these ideas to mark on a number line all integers
x such that:
(i) ƒ xƒ , 5 (ii) ƒ xƒ , 1
(iii) ƒ xƒ $ 5 (iv) ƒ xƒ.21
I am uncertain what you need from us.
Draw a number line, starting at zero, marking 1,2,3,4,5,6,7...10
Somewhere put a b above one of the numbers. To the left of b, between zero and b, put an a above a number.
a) The distance from the origin to b is The number at point b. The distance from the origin to a is the number by a.
The question is, how far is it from a to b?
WEll, if we subtract a from b, we get that distance.
b)I don't understand the symbols above. Sorry.
counting on a number line how do you do that
I need help
I help and on this problem communicate how can you find what each mark represents on a number line
a. Well, if we consider the distance between two points on the number line, we can imagine it as moving from one point to the other. Now, let's say we have two integers a and b. The distance between them can be measured by moving from the point that represents a to the point that represents b. So, in other words, the distance is ƒa 2 bƒ.
b. Ah, the concept of "less than" and "greater than"! Now, if we define "less than" as a being to the left of b on the number line, then it makes sense that b would be to the right of a. It's like saying, "If I'm less than you, then obviously you're greater than me." So, if b is to the right of a, we can say b . a.
Now, let's mark these integers on a number line:
(i) To represent ƒxƒ , 5, we draw a line segment starting from -5 and going up to 5, including the endpoints. This includes all integers between -5 and 5, both inclusive.
(ii) For ƒxƒ , 1, we draw a line segment starting from -1 and going up to 1, including the endpoints. This includes all integers between -1 and 1, both inclusive.
(iii) For ƒxƒ $ 5, we mark all the numbers that are outside the interval -5 to 5, excluding -5 and 5. In other words, any number less than -5 or greater than 5.
(iv) Lastly, for ƒxƒ.21, we mark all the numbers outside the interval -21 to 21, excluding -21 and 21. So, any number less than -21 or greater than 21.
Remember, marking these on a number line will give you a visual representation of the range of integers for each condition!
a. To understand why ƒa - bƒ represents the distance between the points that represent the integers a and b, we need to consider the number line. The distance between two points on a number line is calculated by subtracting their coordinates and taking the absolute value of the result.
In this case, a and b are integers, and their representations on the number line are points. So, to find the distance between these points, we subtract the coordinates of the two points, which gives us a - b. Taking the absolute value of this difference, represented by ƒa - bƒ, ensures that the distance is always positive. Therefore, ƒa - bƒ represents the distance between the points that represent the integers a and b.
b. According to the given definition, "a < b" means that a is to the left of b on the number line. Similarly, "b > a" means that b is to the right of a.
To mark integers x on a number line based on the given conditions:
(i) ƒ xƒ ≤ 5: Mark all integers within a distance of 5 units from the origin (including the origin itself). This would cover the range from -5 to 5 on the number line.
(ii) ƒ xƒ ≤ 1: Mark all integers within a distance of 1 unit from the origin (including the origin itself). This would cover the range from -1 to 1 on the number line.
(iii) ƒ xƒ > 5: Mark all integers outside a distance of 5 units from the origin. This would be all the integers less than -5 or greater than 5 on the number line.
(iv) ƒ xƒ ≥ 21: Mark all integers within a distance of 21 units from the origin (including the origin itself). This would cover the range from -21 to 21 on the number line.