Alternative way of solving problems for page 83.
Solve graphically.
Solution: Let
and
Consider the graphs of
and
as follows: Notice that
is drawn in black and
is drawn in green. We are looking for interval(s)
where
We can see that there are two intersections which
will give us the intervals we need. We are looking for the following
intersections:
and
It is easy to find these two intersections to
be
and
respectively and the answer for
is when
Solve graphically.
Solution: First we rewrite the inequality as follows:
or
Now we define
and
and use the graphical approach we described above
to find the interval(s) for which
We consider the graphs of
(black),
(green) and
(red) as follows: (Notice that these are basic
graphs, which one can figure out easily by hand.) We leave the readers
to find appropriate intersections by hand. The answer is