Quick math question

[sorrel]

My brain is doing a dumb

If you have |x|≥8
That's the same thing as  x≥8 and x≤-8
But is -8≥x≥8 the same thing as the line above?

[Ad Bot]

[Kevso]

If you have |x|≥8
That's the same thing as  x≥8 and x≤-8

no

x≥8 and x≤-8
But is -8≥x≥8 the same thing as the line above?

yes

[sorrel]

no

but isnt that like the expanded form or something if you were to go and try to solve for the inequality?

[Kevso]

but isnt that like the expanded form or something if you were to go and try to solve for the inequality?

Honestly idek I took math a while ago and I don't remember much. I'm just throwing out guesses.

[Placid]

If you have |x|≥8
That's the same thing as  x≥8 and x≤-8

yes. think about this as distance from the origin along the x axis, if you shade a graph of |x| >= 8 that means its at least 8 away (i.e. exactly what you have written)

That's the same thing as  x≥8 and x≤-8
But is -8≥x≥8 the same thing as the line above?

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.

[Red Spy]

this is giving me flashbacks to high school algebra i didn't want

[Master Matthew²]

x is gonna equal me kicking your ass.

[.:FancyPants:.]

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

[sorrel]

Ok thanks. My teacher is weird and was like "I want it in the combined form not two separate inequalities"

[Drydess]

this is giving me flashbacks to high school algebra i didn't want

how can you have flashbacks to the future