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# 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

- SeanLv 52 months agoFavorite 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|

- Anonymous2 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