## Teaching Absolute Value Inequalities – Another Idea

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 $|x|< 4$, threw out numbers and they said “yes” if they were solutions, “no” otherwise Then I drew

to get

Thus $|x|\leq a$ or $|x|< a$ indicates that  the unknown in the middle.  So

Similarly with $|x|> 4$.  Now the unknown is in the tails (extremes).

Thus,

Easy to explain though it took some coaching in the group work before they got comfortable with the middle versus tails idea.