Mathematics, 05.07.2019 19:30 GaudySky

Select the graph for the solution of the open sentence. click until the correct graph appears. |x| > 4

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Answer from: andreamarie2004amg

***********o o**************

<----------(-4)--------(-2)--------(0)--------(-2)----------(4)-------------->

x>4 or x<-4

Step-by-step explanation:

You are looking for numbers that give you a distance, x, greater than 4 from 0. That wouldn't be anything between -4 and 4 because these would all give you a distance less than 4 from 0. So the answer would be to shade everything greater than 4 while also shading everything less than -4.

Here is a number line <-----|-----|-----|-----|-----|-----|-----|-----|-->

-6 -4 -2 0 2 4 6 8

Let's think about this more which of these numbers on this number line would satisfy |x|>4?

Numbers inside the numbers -4 and 4.

Or the numbers on the outside.

Let's try the inside numbers:

-2,02

|-2|>4

2>4 is false which means -2 doesn't satisfy |x|>4

|0|>4

0>4 is false which means 0 doesn't satisfy |x|>4

|2|>4

2>4 is false which means 2 doesn't satisfy |x|>4

We could also try -4 and 4... but these will both give you a distance equal to 4 from 0. And we are looking for greater than.

|-4|>4

4>4 is false which mean -4 doesn't satisfy |x|>4

|4|>4

4>4 is false which means 4 doesn't satisfy |x|>4

Now let's try the numbers on the outside:

-6,6,8

|-6|>4

6>4 is true so -6 does satisfy |x|>4

|6|>4

6>4 is true so 6 does satisfy |x|>4

|8|>4

8>4 is true so 8 does satisfy |x|>4

So what I'm trying to do is convince you more that the only numbers that would satisfy |x|>4 are numbers outside the interval from -4 to 4.

So x>4 or x<-4.

On a number line the solution would look like this:

***********o o**************

<----------(-4)--------(-2)--------(0)--------(-2)----------(4)-------------->

We have holes at -4 and 4 to mean we do not include those numbers. We would have if the inequality read $|x| \ge 4$ . The line underneath this inequality means to include or equals. We do not want to include; we did not have the equal sign. The only difference between the two solutions would be to fill the holes if you $|x| \ge 4$ .