Question

Help with an absolute value inequality problem!

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Answer 1

one problem...

Answer 2

do you know what kinds of numbers | .. | will output?

Answer 3

No...I don't think I understand what you mean

Answer 4

|...| is absolute value of some number

Answer 5

I'm asking you to tell me what kinds of numbers will result after absolute value is applied

Answer 6

Oh ok, no I don't know will output. How do I find that out?

Answer 7

|..| is the distance measurement of .. from 0...
distance is either a positive or 0 number

Answer 8

|x+5| is positive or zero for any x

Answer 9

you have everything great up til
\[|x+5|>\frac{-3}{7}\]

Answer 10

since |x+5| is always either positive or zero that means |x+5| is greater than any negative number

Answer 11

Oh okay! So I wouldn't do the or |x+5| < 3/7 part right?

Answer 12

plug in any x you will see |x+5| is always greater than -3/7

Answer 13

so then my answer would only be x > -38/7?

Answer 14

no your solution is all real numbers
it doesn't matter what you input for x
|x+5| is ALWAYS greater than -3/7 (no matter what x)

Answer 15

oh wait...so then if its always greater than -3/7 would that be all real numbers? sorry if i'm interrupting

Answer 16

Ok! got it thank you so much @freckles!!! Seriously the best

Answer 17

it didn't matter what negative number was on that other side
absolute value of anything is always greater than any negative number
since absolute value of anything always outputs positive number or zero

Answer 18

another problem just for fun:
if you had |x+5|<-3/7
there would be no solution

Answer 19

one last question though...so I checked on mathway and it says the answer would be (3, infinity)... why is that? I don't know how it could be 3.

Answer 20

can't tell you why mathway would say that
mathway if it really said said that when you typed in 7|x+5|+6>3 is incorrect

Answer 21

Ok, that's what i thought too! Thanks for your help again freckles :)

Answer 22

http://www.wolframalpha.com/input/?i=7%7Cx%2B5%7C%2B6%3E3

the result true means it is is a true inequality for all x

Answer 23

Thanks for that! Appreciate it