Question

An absolute equation x+4 <0, I am a bit lost, I thought I understood but now am confused, can someone help please......I thought no solutions am I correct?

Answer 1

| x + 4 | < 0 ?

Answer 2

yes :)

Answer 3

youre in luck, an absolute value can never be negative, so there are no solutions

Answer 4

Excellent thank you so very much :)

Answer 5

$$
\Large |x| \geq 0
$$

Answer 6

So in my justification if I say: The absolute value of x must always be greater than or equal to zero?

Answer 7

no matter what you put inside the absolute value bars, the output will always be positive

Answer 8

or zero

Answer 9

$$
\LARGE | anything | \geq 0

$$

Answer 10

what about \[\left| x-6 \right|\ge0\]

Answer 11

I find these so confusing :(

Answer 12

oh wait ,it must be true for all x

Answer 13

since the absolute value of anything is positive or zero

Answer 14

I was thinking that, so x is an element of all the reals?

Answer 15

yes

Answer 16

let me give you two general solutions

Answer 17

$$
\large \text{assuming that} ~a \geq 0\\

\Large
{|x| \leq a \iff -a \leq x \leq a \\
|x| \geq a \iff x \geq a ~~or~~ x \leq -a


}
$$

Answer 18

$$
\large \text{assuming that} ~a \geq 0\\

\Large
{|x| <a \iff -a<x < a \\
|x|>a \iff x >a ~~or~~ x <-a
\\ \therefore
| x - 6 | \geq 0 \iff x-6 \geq 0 ~~ or ~~ x-6 \leq 0
}
$$

Answer 19

now what is the solution for x >= 6 or x <=6 , that must be any real number

Answer 20

yes, got it, thanks you make much more sense xoxo

Answer 21

it is faster to just say, |x | >= 0 is true for any x

Answer 22

Thank you again :)