At this point, you've isolated the absolute value and can solve this problems for both cases,  and .  Beginning with the first case:

Then for the second case:

Since the absolute value with x in it is alone on one side of the inequality, you set the expression inside the absolute value equal to both the positive and negative value of the other side, 11 and -11 in this case. For the negative value -11, you must also flip the inequality from less than to a greater than. You should have two inequalities looking like this.

and

Add 5 to both sides in each inequality.

and

Divide by -4 to both sides of the inequality. Remember, dividing by a negative will flip both inequality symbols and you should have this.

and

We can set  in the cube of a binomial pattern:

Multiply these complex numbers out in the typical way:

and recall that  by definition. Then, grouping like terms we get

which is our final answer.

Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.

Remember that , so .

Substitute in  for 

Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.

Remember that , so .

Substitute in  for 

Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.

Remember that , so .

Substitute in  for 

Remember that 

So the powers of  are cyclic. This means that when we try to figure out the value of an exponent of , we can ignore all the powers that are multiples of  because they end up multiplying the end result by , and therefore do nothing.

This means that 

Now, remembering the relationships of the exponents of , we can simplify this to:

Because the elements on the left and right have to correspond (no mixing and matching!), we get the relationships: 

No matter how you solve it, you get the values , .

Step 1: Split the  into .

Step 2: Recall that , so let's replace it.

We now have: .

Step 3: Simplify . To do this, we look at the number on the inside.

.

Step 4: Take the factorization of  and take out any pairs of numbers. For any pair of numbers that we find, we only take  of the numbers out.

We have a pair of , so a  is outside the radical.
We have another pair of , so one more three is put outside the radical.

We need to multiply everything that we bring outside: 

Step 5: The  goes with the 9...

Step 6: The last  after taking out pairs gets put back into a square root and is written right after the 

It will look something like this: 

There are two ways to simplify this problem: 

Method 1: 

Method 2: