Write an absolute value inequality that represents the given interval.

Question

Write an absolute value inequality that represents the given interval.

 

<--------------●                           ●               >

<                                                               >

-1   0   1   2   3   4   5   6   7   8   9   10   11

 

|X (+,-) ______| (>,>=,<=,<)|_____

Answer 1

It's hard to tell from your diagram, but I will do the problem as if your endpoints are at 2 and 8.

First off, absolute value deals with a distance from a number. To calculate the "center", all you need to do is take the average of your 2 endpoints. In this case, the average of 2 an 8 is 5.

Next, notice that 5 is 3 units away from both 2 and 8.

 

So in English, your inequality is all the numbers which are greater than or equal to 3 units from 5....that is three or more to the left of 5 are the numbers less than or equal to 2 and 3 or more to the right of 5 are the numbers greater than or equal to 8.

 

So in symbols, you get  ⌈ x-5⌉ ≥ 3. I don't know where you found your absolute value signs, but that is what those brcket looking things are supposed to be. abs(x-5)≥3

 

Hope this helped