Absolute Value Notation?

Rewrite each statement using absolute value notation.

1. The number y is less than three units from the origin.

I don't understand this statement. I see the word origin and quickly think of the point (0,0), which has nothing to do with this exercise, right?

2. The sum of the distances of a and b from the origin is greater than or equal to the distance of a + b from the origin.

2 Answers

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  • Sean
    Lv 5
    2 months ago
    Favorite Answer

    1) if the number is less than three units from the origin then it means the distance on the y axis is -3 < y  < 3 which is |y| < 3

    2) we have two numbers on the number line a and b. the statement says that the algebraic distance of a and of b is  less than or equal to sum of the distances of the two from the origin.

    a and -a are the same distance from the origin

    b and -b are the same distance from the origin

    the distance of the point (a+b) is |a+b|

    distance from the origin of k = |k|

    so

    distance of a from the origin is |a|

    distance of b from the origin is |b|

    if a and b are on the same side of the origin

    the distance of the point a+b

     is |(a) + (b)| or |-(a) - (b) | which is

    the same as |a|+|b|

    if a and b are on opposite sides the total algebraic distance is

    |a - b| or |b - a|  = |a-b|

    putting this together |a+b| is at most  |a|+|b|  and may be less |a-b|

  • Anonymous
    2 months ago

    Why do you think any of this problem must be 2 

    dimensional? if all problem are one-D, then 

    origin is just 0, not (0,0) 

    it says the number y is less than 3 units from the origin. 

    since it just says y , it may be one dimensional    

    y is less than 3 unit from y = 0  

    -3< y< 3 

    for y > 0 ,  y < 3 

    for y < 0 , y> -3  

    multiply both sides by

    -1 and flip > to <  

    -y < 3 and y > 3  which is  

    |y-3|< 0  

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