# How do you solve the inequality 4x+8<0?

Dec 28, 2015

$\textcolor{red}{\text{Comment about format of given solution}}$

$\textcolor{g r e e n}{\text{A bit deep!}}$

#### Explanation:

sente gave the solution $x \in \left(- \infty , - 2\right)$
It appears that there are several conventions regarding notation:

If $x < - 2$ then it takes on all values less than -2 and thus $\underline{\text{excluding -2}}$.

So by using the square bracket notation it would be written as:

" x in[-oo , -2color(white)(.)[color(white)(...)"..... where the reversed square bracket  [ -> " not inclusive"

$\textcolor{red}{\text{However, it appears that this is not correct}}$

We have: The presented solution of $x \in \left(- \infty , - 2\right)$ when compared to first line given in Wikipedia gives cause for some debate.

The Wikipedia table $\textcolor{red}{\underline{\text{implies}}}$ that $x \in \left(\infty , - 2\right)$ is such that $x < - 2$ which is absolutely true but unfortunately it also implies that $\infty < x$ which is not true.

However I have been given some guidance by a couple of very informed Mathematicians that the

$\textcolor{g r e e n}{\text{the use of curved brackets is indeed correct for this context.}}$

$\textcolor{red}{\text{By some conventions that I was not previously aware of}}$
$\textcolor{red}{\text{it would not be correct to write}}$
$\textcolor{red}{\left[- \infty , - 2\right) \to \left\{x \in \mathbb{R} | - \infty \le x < - 2\right\}}$.

I am advised that this is because the use of [ is only applicable if $x \in \mathbb{R}$. The problem is that $\infty \notin \mathbb{R}$ so the use of [ is not permitted.