no
yes
it's exactly the opposite of what kevso said here
yes, |x|≥8 is exactly the same as x≤-8 and x≥8|x|≥8 would be all the numbers on the number line that you can plug in for x and still get something greater than or equal to 8. that's
no, -8≥x≥8 is exactly the opposite from x≤-8 and x≥8
-8≥x≥8 would be all the numbers on the number line between and including -8 and 8. x≤-8 and x≥8 is pretty much the opposite, except in both cases you include 8 and -8.quick edit:
ok, i thought i misread something because i wouldn't expect placid to answer yes for the second question
yeah,
i mean i guess technically yes? but no one writes it this way in actual math because if you graph it out you're describing two separate intervals, (-inf, -8] and [8, inf) which makes more sense as two separate inequalities. we would use an expression like that for something like |x| <= 8.
this is right and i'm wrong
in fact the reason why they probably don't write -8≥x≥8 is because it'd be so easily confused for -8≤x≤8, which is exactly what i just did