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# modulus inequality

1. | 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
2. (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
You should find a graph useful
Attached Images

3. 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:
Show
Note this may not be the best (or even correct) way of approaching this
4. (Original post by steve2005)
You should find a graph useful
that was useful! picturing it like that definitely helps thankyou!

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