, so  must be positive. Therefore, since , it follows that , so  must be positive, and

If  is negative or zero, it is the least of the three. If  is positive, then the statement becomes

,

and  is still the least of the three. Therefore,  must be the least of the three, and the correct choice is "None of the other responses is correct."

When dealing with absolute value bars, it is important to understand that whatever is inside of the absolute value bars can be negative or positive. This means that an inequality can be made.

In this particular case if , then, equivalently, 

From here, isolate the variable by adding seven to each side.

In interval notation, this is .

First you plug in  for  and squre it.  

This gives the expression  which is equal to .  

Since the equation is within the absolute value lines, you must make it the absolute value which is the amount of places the number is from zero.  

This makes your answer .

The absolute value of a number is its distance from zero.  Absolute value is represented with  or absolute value bars .  To solve this absolute value equation remove the absolute value bars and set the equation equal to positive and negative eleven.

 and  are the two values of  which make this statement true.

and

Remember, because Absolute Value measures the distance from zero, the absolute value of a number whether negative or positive is always                    non-negative.

Absolute value measures distance from that number to the point of origin or zero.

However, there is a negative sign outside the Absolute value bars, which indicates the multiplication by 

 becomes 

Therefore  is the correct solution.

The first step to solving is to use the Order of Operations.

The absolute value  of a real number x is the non-negative value of x without regard to its sign.  The absolute value of a number is the distance of that number from the point of origin or zero on a number line.

To solve this Absolute Value inequality, remove the Absolute Value bars and create two linear inequalities.

Then, using the Order of Operations and the method for solving multi-step equations solve.

First inequality:

Second inequality:

The solution to   consists of the two intervals  and  .  This pair of inequalities is the solution.

To solve this Absolute Value inequality, remove the Absolute Value bars and create two linear inequalities.

 and

Then solve each of the inequalities.

First inequality:

Second inequality:

The solution to   consists of the two intervals  and  .  This pair of inequalities is the solution.

To solve this Absolute value inequality, remove the absolute value bars and create two linear inequalities and solve.

The solution to  consists of the two intervals  and  .

This pair of inequalities is the solution.

Step One: Order of Operations

The absolute value of  is   However, because there is a negative sign outside the Absolute value bars, you would multiply the  by  to get the solution.

The correct answer is