We begin by solving the equation for its zeros. This is done by changing the  sign into an  sign. 

Since we know the zeros of the equation, we can then check the areas around the zeros since we naturally have split up the real line into three sections :

First we check 

Therefore, the first interval can be included in our answer. Additionally, we know that  satisfies the equation, therefore we can say with certainty that the interval  is part of the answer. 

Next we check something in the second interval. Let , then

Therefore the second interval cannot be included in the answer.

Lastly, we check the third interval. Let , then

Which does satisfy the original equation. Therefore the third interval can also be included in the answer. Since we know that  satisfies the equation as well, we can include it in the interval as such: 

Therefore, 

Method 1:

1) Multiply-out the left side then rewrite the inequality as an equation:

2) Now rewrite as a quadratic equation and solve the equation:

3) Next set up intervals using the solutions and test the original inequality to   see where it holds true by using values for  on each interval.

4) The interval between  and  holds true for the original inequality.

5) Solution: 

Method 2:

Using a graphing calculator, find the graph.  The function is below the x-axis (less than ) for the x-values .  Using interval notation for , .

Method 3:

For the inequality , the variable expression in terms of is less than , and an inequality has a range of values that the solution is composed of.  This means that each of the solution values for  are strictly between the two solutions of .  'Between' is for a 'less than' case, 'Outside of' is for a 'greater than' case.

1) Write  as two simple inequalities:

2) Solve the inequalities:

3) Write the final solution as a single compound inequality:

 For interval notation:

4) Now graph:

In order to solve this equation, we must first isolate the absolute value. In this case, we do it by dividing both sides by  which leaves us with:

When we work with absolute value equations, we're actually solving two equations. So, our next step is to set up these two equations: 

 and 

In both cases we solve for  by adding  to both sides, leaving us with

 and 

This can be rewritten as 

When we work with absolute value equations, we're actually solving two equations: 

 and 

Adding  to both sides leaves us with: 

 and 

Dividing by  in order to solve for  allows us to reach our solution:

 and 

Which can be rewritten as:

In order to solve for  we must first isolate the absolute value. In this case, we do it by dividing both sides by 2:

As with every absolute value problem, we set up our two equations:

 and 

We isolate  by adding  to both sides:

 and 

Finally, we divide by :

 and 

Our first step in solving this equation is to isolate the absolute value. We do this by dividing both sides by 

.

We then set up our two equations:

 and .

Subtracting 4 from both sides leaves us with

 and .

Lastly, we multiply both sides by 2, leaving us with :

 and .

Which can be rewritten as:

We first need to isolate the absolute value, which we can do in two steps:

1. Add 2 to both sides:

2. Divide both sides by 4:

Our next step is to set up our two equations:

 and 

We can now solve the equations for  by subtracting both sides by 8:

 and 

and then dividing them by 5:

 and 

Which can be rewritten as: 

First we need to get the expression with the absolute value sign by itself on one side of the inequality. We can do this by subtracting seven from both sides.

Next we need to set up two inequalities since the absolute value sign will make both a negative value and a positive value positive.

From here, subtract thirteen from both sides and then divide everything by four.

First we need to get the expression with the absolute value sign by itself on one side of the inequality. We can do this by dividing both sides by three. 

We now have two equations:

  and 

So, our solution is