distance and notation show all work

Question

1a. Which of the following represents the distance between 12.4 and – 6.9 on the number line? 

     A. | 12.4 | – | -6.9 |

     B. | -6.9 - 12.4|

     C. | 12.4 - 6.9 |

     D. | –6.9| – | 12.4|

 

1b. Find the distance. Show your work.

 

2. Write the interval notation corresponding to the set notation {x | x ≥ – 4}.

Answer 1

1a) B

 

1b) l -6.9-12.4 l=l -19.3 l=19.3 units on the number line

Look at it this way: if you were at -6 on the number line and had to get to +12 on the number line you would move 6 units to the right to get to 0 and then move another 12 units to the right to get to +12 for a total of

6+12 or 18 units altogether

 

2) [-4,∞)

Answer 2

Theresa,

 

Distance on the number line between a an b is given as 

 

|a - b|  or |b - a|

 

so for  12.4 and - 6.9

 

It will be either  |12.4 - (-6.9)|  or  |-6.9 - 12.4|

 

Since we only paying attention to absolute number of the result it does not matter if we have  

 

|12.4 + 6.9|  or  |-6.9 -12.4|

 

so your right choice is  given  |-6.9 -12.4|

 

1b. Find the distance. Show your work.

 

|12.4 + 6.9| or |-6.9 -12.4|

 

|19.3| or |-19.3| = 19.3

2. Write the interval notation corresponding to the set notation {x | x ≥ – 4}.

 

x starts from negative 4 and continues infinitely

 

[-4, ∞ )