absolute value inequalities (easy answer)

Question

which is an AND statement and which is an OR statement; |x|>? and |x|<?

 

so on a number line one of the equations above has two points shaded outwards, with a blank spot inbetween the two spots. The other has two points shaded inwards, the outside of both points is blank, so they are connected. I know there are special circumstances where {x:xE|R}(all real numbers) but I just want to know which is which.

 

Thank you in advance!

Answer 1

which is an AND statement and which is an OR statement; |x|>? and |x|<?

so on a number line one of the equations above has two points shaded outwards, with a blank spot inbetween the two spots. The other has two points shaded inwards, the outside of both points is blank, so they are connected. I know there are special circumstances where {x:xE|R}(all real numbers) but I just want to know which is which.
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ok:

 

the 1st one - it's the "shaded outside" case, how you say. here, solution will be any point EITHER in right shade OR in a left one. there can't be AND - no way. just or ... or...

 

whereas in 2nd case, when "shade is inward", any solution included betwin the endpoints of your interval; that is to say, the solution X is SAME TIME less than upper/higher/greater X  AND it must be greater than the lower endpoint of interval. you cannot use "or" here ... is this enough? message if questions:)