Having my younger son try out Matt Enlow’s algebra inequality problem

I saw an interesting tweet from Matt Enlow earlier today and thought it would be fun to have my younger son try out the problem:

It doesn't matter how many times we go over it, SO many of my students will still start to solve an inequality like x ≤ (2x+3)/(x+4) by multiplying both sides by x+4.

I guess they've been… "well-trained"? 😑

— Matt Enlow (@CmonMattTHINK) June 5, 2021

One bit of hesitation I had was that I didn’t know if my son had seen rational functions in school or not, so we started with an overview of the problem just to make sure that he understood it:

In the first video he made some progress on the problem in the case when x > -4. Now we finished up that piece of the problem:

Now he tackled the case when x < -4. This part was not as difficult since we’d done most of the necessary work already:

Finally, we went to the computer to look at a graph of both equations. Here he talks about how these graphs help us see the solution to the original equation:

I liked this problem and was happy that my son was able to work through it. Definitely a nice problem for students learning algebra to think through.