|x|>S what is it on a number line

Question

this is probably super easy but I can't wrap my head around this can somebody graph this on a number line. I am trying to understand what $|x|>S$ looks like on a number line.

Answer 1

For example, $|x|>2 $ looks like this:

If you try filling in some numbers for $x$, and think about what $|x|$ then becomes, you will see why.

Ask me if you need more clarification!

Answer 2

Note that $|x| \geq 0$, the same goes for $S $ as well. So, why don't you just draw a graph or look it up using Desmos?

Answer 3

On the real number line these are numbers from -infinity to -S and from S to +infinity

Answer 4

For $S\ge 0$ it is equivalent to $x\lt-S\lor x\gt S$ so $x\in(-\infty,-S)\cup(S,\infty)$. Can you draw that? Watch out for the case $S=0$.

If $S\lt 0$, the solution set is all of the real line, i.e.$(-\infty,\infty)$. Can you draw that?