I was typing out solutions to an Algebra 2 assessment the other day. Question 3 on the assessment asks students to solve an equation involving absolute value. I began my solution with this…

…and then launched into an algebraic confirmation of that solution.

Now on the one hand, throwing a Desmos-generated graph into a “detailed solutions” handout is a great move because, well, just look at it. It’s beautiful. And hey! Multiple representations! Plus it took about 30 seconds from start to finish. No brainer, right?

Well, on the other hand, including something like that is dangerous, because when you find yourself writing the solutions to questions 6 and 7 (as I did just a few moments later), and these questions ask for a graphical display of the solution to a one-variable linear inequality… Well now you’ve tasted greatness, and you won’t settle for anything else.

There’s just one problem: Desmos doesn’t do linear inequalities in one variable.

Okay, that last sentence is actually not true. Desmos *will* graph linear inequalities in one variable. You just have to ask nicely. Check it out:

I imagine I’m not the only one to do this (and it would still be pretty cool if Desmos would add one-variable number line graphing functionality… Pretty please?), but I thought I’d share how to do it anyway, just in case anyone is curious (and wants to give one-variable graphing a little Desmos-love).

# Here’s How

The best way to explain is to throw a few images in here and let them do the talking. Drop me a line on Twitter (@mjfenton) or in the comments if you have any questions (or tips for how to make this even easier or more awesome). Or if your name is Eli and you have a new feature to announce.

## Comments 5

Michael

Are the y inequalities in the last few screenshots simply there to scale the window you are looking at? What would Desmos do without those y limitations? I’ll be trying this myself now that I thought of the question.

Author

@mrdardy, the y inequalities are there to provide the shading between the endpoints. Without that line, I would just be staring at two points on the x-axis. What I’ve really done is create a shaded rectangle, but the height is small enough that it just looks like a thick line.

Thank you! This is so helpful!

Hello Michael,

Thank you for showing how to graph one variable inequality. I have a question, I want to be able to drag the point and shaded area along the x axis. In graph 3 I turned on the drag (horizontal) feature for the point (4,0). But for graph 4, it disables the drag if the point (-2,0) is an open circle. Any suggestions on how to over come this? Appreciate your help. Thanks Shriya.

Hi Shriya, thanks for stopping by, and for your question! What if the movable point was separate from the display? Here’s my attempt: https://www.desmos.com/calculator/czghfmvonk