# Thread: [SOLVED] Absolute Values and Inequalities

1. ## [SOLVED] Absolute Values and Inequalities

greater than or equal to 0

x can be any real number, because the absolute value of any number is bigger or equal to 0.

3. Originally Posted by mathhomework
greater than or equal to 0

x can be any real number, because the absolute value of any number is bigger or equal to 0.
$\displaystyle |x + 4| \ge 0$

$\displaystyle \Rightarrow x+4 \ge 0$

$\displaystyle \Rightarrow x\ge -4$ .................................(1)

OR

$\displaystyle |x + 4| \ge 0$

$\displaystyle \Rightarrow -(x+4) \ge 0$

$\displaystyle \Rightarrow -x\ge 4$

$\displaystyle \Rightarrow x\le -4 ...................................(2)$

from (1) and (2), x can have all real values. So,

$\displaystyle x\in \mathbb{R}$

4. I'm sorry, I posted that wrong, it is supposed to be less than or equal to zero.

$\displaystyle |x| \ge 0$ for all real $\displaystyle x$.
thus, $\displaystyle |x| \le 0$ only makes sense if $\displaystyle |x| = 0$
thus we want $\displaystyle x + 4 = 0 \implies x = -4$ is our only solution.