Let the number be
.
The cube of a number be less than the number means
.
Now solve the inequality is
.
Rewrite the inequality as
.
The function
.
First solve the equation
.

To find the solution of the inequality
, use the intervals
,
,
and
.
| Interval | \Number chosen | \value of ![]() | \
Conclusion | \
![]() | \
![]() | \
![]() | \
Negative | \
![]() | \
![]() | \
![]() | \
Positive | \
![]() | \
![]() | \
![]() | \
Negative | \
![]() | \
![]() | \
![]() | \
Positive | \
From the above table, conclude that
for all numbers
for which
or
.
Thus, the solution set is
.
Therefore, the solution of
is
or in interval notation
.
;
.