The inequality is .
The radical is defined for
.
The radical is defined for
.
Consider .
Consider .
.
The domain of the equation is restricted to .
Now consider the original inequality equation .
Squaring on both sides.
\Make sure to completely isolate the radical before squaring both sides of the inequality. Note change in sign.
\.
Now squaring on both sides.
\.
.
.
.
.
Consider .
The above equation is in the form of .
Where .
The quadratic formula is .
Now subustiute the values of in the above equation.
Therefore has
real zeros at
and
.
Create a sign chart using the values and
.
Note : The solid circle denote that the value are included in the solution set.
\Observe the sign chart :
\The set of value of denoted in pink color represents the solution set.
Determine whether is positive or negative on the test intervals.
Test intervals are and
.
If then
.
If then
.
If then
.
The solutions of are
values for which
is negitive or equal to
.
The solution set is .
The domain of the equation is restricted to .
Create a sign chart that includes this restriction.
\When solving inequalities that involve raising each side to a power to eliminate a radical, it is important to test every interval using the original inequality.
\Substitute a value in each test interval into the original inequality to determine if
is a solution.
The original inequality equation is .
If then
.
If then
.
If then
.
If then
.
Therefore the solution set is .
The Solution set of is
.