I am still searching for a good way to teach the basic structure for solving absolute value inequalities. Here are two models I posted earlier – with lots of arrows and with a weird formula pattern. This time I went for total simplification – just two associations to understand and memorize.
I started as usual with my “join the club” exercise where everyone lined up and stepped forward if their number satisfied the given inequality. Also as usual I emphasized that either the middle or the tails stepped forward. Then I drew a number line like this.
And we filled in the blanks with either “<” or “>”. They soon figured out that “<” was used in all cases – smallest on left, largest on right. I then wrote , threw out numbers and they said “yes” if they were solutions, “no” otherwise Then I drew
Thus or indicates that the unknown in the middle. So
Similarly with . Now the unknown is in the tails (extremes).
Easy to explain though it took some coaching in the group work before they got comfortable with the middle versus tails idea.