GRE Subject Test: Math : Absolute Value Inequalities

Study concepts, example questions & explanations for GRE Subject Test: Math

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Example Questions

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Example Question #51 : Classifying Algebraic Functions

Possible Answers:

 or 

Correct answer:

Explanation:

The first thing we must do is get the absolute value alone: 

When we're working with absolute values, we are actually solving two equations:

     and 

Fortunately, these can be written as one equation:

If you feel more comfortable solving the equations separately then go ahead and do so.

              To get  alone, we added  on both sides of the inequality sign

 

Example Question #52 : Classifying Algebraic Functions

Possible Answers:

or

or

or

Correct answer:

or

Explanation:

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

Example Question #1 : Absolute Value Inequalities

Possible Answers:

 and 

 and 

There is no solution.

 and

Correct answer:

 and 

Explanation:

 

 

The correct answer is  and 

Example Question #54 : Classifying Algebraic Functions

Possible Answers:

There is no solution.

Correct answer:

There is no solution.

Explanation:

Because Absolute Value must be a non-negative number, there is no solution to this Absolute Value inequality.

Example Question #55 : Classifying Algebraic Functions

The weight of the bowling balls manufactured at the factory must be  lbs. with a tolerance of  lbs.  Which of the following absolute value inequalities can be used to assess which bowling balls are tolerable?

Possible Answers:

Correct answer:

Explanation:

The following absolute value inequality can be used to assess the bowling balls that are tolerable:

Example Question #56 : Classifying Algebraic Functions

Possible Answers:

 and 

 and 

 and 

There is no solution.

Correct answer:

 and 

Explanation:

 

 

The correct answer is  and 

Example Question #57 : Classifying Algebraic Functions

Possible Answers:

 and 

 and 

 and 

 and 

Correct answer:

 and 

Explanation:

 

 

 

 

The correct answer is  and 

 

 

 

 

Example Question #58 : Classifying Algebraic Functions

Possible Answers:

 and

 and 

 and

There is no solution.

Correct answer:

 and 

Explanation:

 

 

The correct answer is  and

Example Question #59 : Classifying Algebraic Functions

Possible Answers:

    and

 and 

  and   

There is no solution.

Correct answer:

    and

Explanation:

 

The correct answer is   and 

Example Question #60 : Classifying Algebraic Functions

Possible Answers:

 and  

 and 

 and  

 and 

Correct answer:

 and  

Explanation:

 

 

The correct answer is  and 

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