Rewrite Using Absolute Value Notation

Set 1.2
Questions
40, 42, 44, 46, 48
David Cohen

Rewrite each statement using absolute value notation.

40. The distance between x and 1 is less than 1/2.

| x - 1 | < 1/2

42. The distance between x and 1 exceeds 1/2.

| x - 1 | > 1/2

44. The distance between x^3 and -1 is at most 0.001.

| x^3 -(-1) |<= 0.001

| x^3 + 1 | <= 0.001

46. The number y is less than one unit from the number t.

| y - t | < 1

48. 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.

| a + b | => | a + b - 0 |

| a + b | => | a + b |

You say?

 

all above is correct except 48 which should be:

the sum of the distances of a and b from the origin would be:
|a|+|b|
and the distance of the sum a + b from the origin is:
|a+b|
and so we would write:
|a|+|b| ≥ | a+b|

 

I got 48 wrong. Only one incorrect answer.