Number Line & Intervals (Part 1)

[mathdad]

The set of real numbers satisfying the given inequality is one or more intervals on the number line. Show the intervals on a number line.

(A) |x| < 2

(B) |x| > 0

For (A), I must plot -2 < x < 2 on the number line. In interval notation it is written (-2, 2). Is this right?

For (B), we have the fact that x < 0 or x > 0. Does this mean there is an arrow to the left and right of zero on the number line? I do not understand why, in interval notation, we write (-infinity, 0) and (0, infinity).

 

[MarkFL]

This is how I would draw the intervals:

a)

\begin{tikzpicture}[scale=2.5]
\draw[very thick] (-2,0) -- (2,0);
\path [draw=black, fill=white, thick] (-2,0) circle (2pt);
\path [draw=black, fill=white, thick] (2,0) circle (2pt);
\draw[latex-latex] (-2.5,0) -- (2.5,0) ;
\foreach \x in {-2,-1,0,1,2}
\draw[shift={(\x,0)},color=black] (0pt,3pt) -- (0pt,-3pt);
\foreach \x in {-2,-1,0,1,2}
\draw[shift={(\x,0)},color=black] (0pt,0pt) -- (0pt,-3pt) node[below]
{$\x$};
\end{tikzpicture}

b)

\begin{tikzpicture}[scale=2.5]
\path [draw=black, fill=white, thick] (0,0) circle (2pt);
\draw[latex-latex] (-2.5,0) -- (2.5,0) ;
\draw[->,thick] (0,0) -- (2.25,0);
\draw[->,thick] (0,0) -- (-2.25,0);
\foreach \x in {-2,-1,0,1,2}
\draw[shift={(\x,0)},color=black] (0pt,3pt) -- (0pt,-3pt);
\foreach \x in {-2,-1,0,1,2}
\draw[shift={(\x,0)},color=black] (0pt,0pt) -- (0pt,-3pt) node[below]
{$\x$};
\end{tikzpicture}

 

[mathdad]

This is how I would draw the intervals:

a)

\begin{tikzpicture}[scale=2.5]
\draw[very thick] (-2,0) -- (2,0);
\path [draw=black, fill=white, thick] (-2,0) circle (2pt);
\path [draw=black, fill=white, thick] (2,0) circle (2pt);
\draw[latex-latex] (-2.5,0) -- (2.5,0) ;
\foreach \x in {-2,-1,0,1,2}
\draw[shift={(\x,0)},color=black] (0pt,3pt) -- (0pt,-3pt);
\foreach \x in {-2,-1,0,1,2}
\draw[shift={(\x,0)},color=black] (0pt,0pt) -- (0pt,-3pt) node[below]
{$\x$};
\end{tikzpicture}

b)

\begin{tikzpicture}[scale=2.5]
\path [draw=black, fill=white, thick] (0,0) circle (2pt);
\draw[latex-latex] (-2.5,0) -- (2.5,0) ;
\draw[->,thick] (0,0) -- (2.25,0);
\draw[->,thick] (0,0) -- (-2.25,0);
\foreach \x in {-2,-1,0,1,2}
\draw[shift={(\x,0)},color=black] (0pt,3pt) -- (0pt,-3pt);
\foreach \x in {-2,-1,0,1,2}
\draw[shift={(\x,0)},color=black] (0pt,0pt) -- (0pt,-3pt) node[below]
{$\x$};
\end{tikzpicture}

Cool. Is my math work correct, Mark? You must have a computer math software.

 

[MarkFL]

Cool. Is my math work correct, Mark? You must have a computer math software.

Yes, your math is all good. (Star)

For the diagrams, I used our TikZ feature. (Yes)

Click on the images to see the code I used to generate them. :D

 

[mathdad]

Yes, your math is all good. (Star)

For the diagrams, I used our TikZ feature. (Yes)

Click on the images to see the code I used to generate them. :D

I will check out Tikz feature. Does it also apply to cell phones?

 

[MarkFL]

I will check out Tikz feature. Does it also apply to cell phones?

As far as I know, but I don't use any mobile devices so I can't tell you for sure. :)

 

[mathdad]

As far as I know, but I don't use any mobile devices so I can't tell you for sure. :)

I want to thank you for being so attentive to my questions and for not passing judgement like a few others do. I joined this site to help me become a better math person. I enjoy math. I love precalculus.

Math helps me forget about the problems of life. I help elementary school students with math homework online and through in-person tutoring when time allows. I also help middle school students. It is because of websites like this one that I feel my math skills have greatly increased. I have more work to do in terms of word problems but one section at a time.