The last part of our unit on inequalities covers absolute value special cases and word problems. You can read about part 1 here and part 2 here.

##### Absolute Value Inequality Special Cases

To introduce solving absolute value inequalities that have no solution or all real numbers as the answer, I tried a couple different things this year. In a couple classes I put this up on the board and we talked about each of them, which is what I had done in the past.

In another class I put the following up on the board and asked how we could write an inequality that would never be true.

###### |x|______________

Then I asked how we could write an inequality that would never be true. Once students gave me answers for that and understood, we talked about if it mattered what was inside the absolute value bars. Both ways worked fine, but I almost think I liked think I liked this new way better. I liked that students were coming up with the inequalities.

The next day I started with the following warm-up problem. I always like to include absolute value inequalities that don’t have all real numbers or no solution as the answer so that students don’t forget what they already knew about those types of problems.

Here is the link to download a worksheet with these types of problems.

I also created an Open Middle type problem for these types of inequalities. You can download it here.

##### Absolute Value Inequality Word Problems

One of the things that my students need to know is how to solve word problems involving absolute value inequalities. In the past, I just jumped into these types of problems, but this year I took a day to go over setting up the absolute value inequalities given a graph. The day before this I had each student solve an absolute value inequality to use as this introduction. You can download the problems I used here.

I took several of these and had students find the midpoint of each graph and the distance from the midpoint. Then students looked for a pattern.

Then I had students practice writing absolute value inequalities when given a graph and practice finding the midpoint of the graph and distance from the midpoint when given an absolute value inequality.

The next day when we got to solving word problems went so much better than it did last year having spent a day on this ahead of time.

You can download the test review here.