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modulus inequality

| 4-x^2 | < 3

i know that this means |4-x^2| <± 3 and can solve it to get x>± sqrt7 and x>±1

the answer wants -sqrt7<x<-1 and 1<x<sqrt7

can somebody explain this for me please? thanks :smile:
(edited 12 years ago)
Reply 1
Avatar for steve2005
steve2005
17
Original post by rub em out
| 4-x^2 | < 3

i know that this means |4-x^2| <± 3 and can solve it to get x>± sqrt7 and x>±1

the answer wants -sqrt7<x<-1 and 1<x<sqrt7

can somebody explain this for me please? thanks :smile:


You should find a graph useful
Screen shot 2011-06-10 at 20.11.28.png20.0KB
Reply 2
Avatar for Spungo
Spungo
10
You can break it up in to 2 inequalities, i.e:
4 - x^2 < 3 [1]
4 - x^3 > -3 [2]

Then for [1]
x^2 > 1
And this is only satisfied when |x| > 1, I.E. x > 1 and x < -1
[2] is similar.

Spoiler

Reply 3
Avatar for rub em out
rub em out
OP
7
Original post by steve2005
You should find a graph useful


that was useful! picturing it like that definitely helps :smile: thankyou!

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