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

Answer:***********o                                                         o**************<----------(-4)--------(-2)--------(0)--------(-2)----------(4)-------------->x>4 or x<-4Step-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|>4We 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|>4Now 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|>4So 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 [tex]|x| \ge 4[/tex].  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 [tex]|x| \ge 4[/tex].