Interval Notation

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January 10th 2010, 04:58 PM
BadMaterial

Interval Notation

Need help on solving this absolute value inequality using interval notation!!

2|x +6| + 4 > 1
January 10th 2010, 05:06 PM
Prove It

Quote:

Originally Posted by BadMaterial

Need help on solving this absolute value inequality using interval notation!!

2|x +6| + 4 > 1

This doesn't really make any sense...

$|x + 6| \geq 0$ for all $x$ .

So that means that

$2|x + 6| \geq 0$ for all $x$

$2|x + 6| + 4 \geq 4$ for all $x$ .

Since it is always no less than 4, it must always be greater than 1...

So $x \in (-\infty, \infty)$ ...
January 10th 2010, 05:24 PM
pomp

Quote:

Originally Posted by Prove It

$|x + 6| \geq 0$ for all $x$ .

So that means that

$2|x + 6| \geq 2$ for all $x$

$2|x + 6| + 4 \geq 6$ for all $x$ .

I think you meant to say

$2|x + 6| \geqslant 0$

$2|x + 6| + 4 \geqslant 4$

(The result still remains true though BadMaterial)
January 10th 2010, 05:28 PM
Prove It

Thanks.

Edited.

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