Interval Notation

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

2|x +6| + 4 > 1

Quote:

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Originally Posted by BadMaterial

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

2|x +6| + 4 > 1

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This doesn't really make any sense...

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


So that means that

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

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


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


So $\displaystyle x \in (-\infty, \infty)$...

Quote:

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Originally Posted by Prove It

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


So that means that

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

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

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I think you meant to say

$\displaystyle 2|x + 6| \geqslant 0$

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

(The result still remains true though BadMaterial)

Thanks.

Edited.