The functions are
and
.
Given
.
.
Write the inequality so that the expression
is on the left side and zero is on the right side.
.
.
The function is
.
Determine the real zeros (
-intercepts of the graph ) of
and the real numbers for which
is undefined.
The zeros of the function are the values of
for which
.
.
Let
.

Earlier we considered
.
\
The zeros of
are
and
.
Since
are imiginary roots these are not to be considered.
Therefore the zeros of the function are
and
.
Use the zeros found in Step 2 to divide the real number line into intervals.
\The function intervals are
and
.
Since there are
real zeros, divide the
- axis into three intervals.
\
Choose a number for
in each interval and evaluate
.
| Interval | \ \
\ \
\ | \
\
\
| \
Conclusion | \
| \
\
| \
\
| \
\
| \
Positive | \
| \
| \
\
| \
\
| \
\
Negative \ | \
![]() | \
\
| \
\
| \
Positive | \
\
Graph :
\(1) Draw the coordinate plane.
\(2) Graph the functions
and
on the same graph.

Observe the graph
is below to the graph of the function
.
The inequality function interval is
at
.
\
\
The Solution of algebraical inequality
are in the intervals
.
Graph :
\
.