# Interval Notation

• Jan 10th 2010, 04:58 PM
Interval Notation
Need help on solving this absolute value inequality using interval notation!!

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

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

2|x +6| + 4 > 1

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 $\displaystyle x \in (-\infty, \infty)$...
• Jan 10th 2010, 05:24 PM
pomp
Quote:

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 $\displaystyle x$.

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)
• Jan 10th 2010, 05:28 PM
Prove It
Thanks.

Edited.