Call Now to Set Up Tutoring:

(888) 888-0446

GRE Subject Test: Math : Absolute Value Inequalities

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

Create An Account

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #232 : Gre Subject Test: Math

$5\left | x-7\right |+14<39$

Possible Answers:

2< x<12

x> 12 or x< 2

2< x

x<12

Correct answer:

2< x<12

Explanation:

The first thing we must do is get the absolute value alone: $5\left | x-7\right |+14<39$

$5\left | x-7\right |<25$

$\left | x-7\right |<5$

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

x-7<5 and x-7> -5

Fortunately, these can be written as one equation:

-5< x-7<5

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

2< x<12

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

Report an Error

Example Question #1 : Absolute Value Inequalities

$\left | y\right | + 18 \leq 11.3$

Possible Answers:

There is no solution.

$y\geq 6.7$

$y\leq -6.7$

$y\leq 29.3$

Correct answer:

There is no solution.

Explanation:

$\left | y\right | + 18 \leq 11.3$

$\left | y\right |\leq -6.7$

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

Report an Error

Example Question #1 : Absolute Value Inequalities

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:

$\left | w-3 \right | \leq 8$

$\left | w-3 \right |\geq 8$

$\left | w-8\right | \leq 3$

$\left | w-8\right | \geq 3$

Correct answer:

$\left | w-8\right | \geq 3$

Explanation:

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

$\left | w-8\right |\geq3$

Report an Error

Example Question #234 : Gre Subject Test: Math

$4\left |(x+0.3)\right | - 3 < 11$

Possible Answers:

x<-3.2 and x> -2.3

x> 3.2 and x< -2.3

x<3.2 and x> -2.3

There is no solution.

Correct answer:

x<3.2 and x> -2.3

Explanation:

$4\left |(x+0.3) \right | - 3< 11$

4x + 1.2 - 3 < 11

4x -1.8<11

4x -1.8 +1.8<11 + 1.8

4x< 12.8

$\frac{4x}{4} < \frac{12.8}{4}$

x<3.2

4x + 1.2 - 3> -11

4x - 1.8> -11

4x - 1.8 + 1.8> -11 + 1.8

4x > -9.2

$\frac{4x}{4}>\frac{-9.2}{4}$

x> -2.3

The correct answer is x<3.2 and x>2.3

Report an Error

Example Question #2 : Absolute Value Inequalities

$\left | 6+x\right |-4 < 0$

Possible Answers:

x<2 and x>10

x>-2 and x< -10

x<-2 and x> -10

x< 2 and x > 10

Correct answer:

x<-2 and x> -10

Explanation:

$\left | 6+x\right | -4 < 0$

6 + x -4 < 0

6 + x < 4

6-6 + x < 4-6

x< -2

6 + x > -4

6-6 + x > -6-4

x>-10

The correct answer is x< -2 and x>-10.

Report an Error

Example Question #1 : Absolute Value Inequalities

$\left | \frac{x-6}{2} \right |\leq 3$

Possible Answers:

$x\geq 0$ and $x\leq 12$

There is no solution.

$x\geq 0$ and $x\leq 12$

$x\leq 0$ and $x\geq12$

Correct answer:

$x\geq 0$ and $x\leq 12$

Explanation:

$\left | \frac{x-6}{2} \right |\leq3$

$\frac{2}{1} \left | \frac{x-6}{2} \right | \leq 2\times3$

$x-6 \leq 6$

$x\leq 12$

$\frac{2}{1} \left | \frac{x-6}{2} \right | \geq 2 \times -3$

$x-6 \geq -6$

$x\geq 0$

The correct answer is $x\leq12$ and $x\geq 0.$

Report an Error

Example Question #1 : Absolute Value Inequalities

$\left | x-5\right |\leq7$

Possible Answers:

$x\leq-12$ and $x \geq 2$

$x\geq12$ and $x\leq -2$

x<12 and x> -2

$x\leq12$ and $x\geq-2$

Correct answer:

$x\leq12$ and $x\geq-2$

Explanation:

$\left | x-5\right |\leq 7$

$x-5 \leq 7$

$x-5 + 5 \leq 7 +5$

$x\leq 12$

$x-5 \geq -7$

$x-5 +5 \geq -7 +5$

$x\geq -2$

The correct answer is $x\leq12$ and $x\geq -2.$

Report an Error

Example Question #3 : Absolute Value Inequalities

A type of cell phone must be less than 9 ounces with a tolerance of 0.4 ounces. Which of the following inequalities can be used to assess which cell phones are tolerable? (w refers to the weight).

Possible Answers:

$\left | w-0.4\right | \geq 9$

$\left | w-9\right | \geq 0.4$

$\left | w-0.4\right | \leq 9$

$\left | w-9\right | \leq 0.4$

Correct answer:

$\left | w-9\right | \leq 0.4$

Explanation:

The Absolute Value Inequality that can assess which cell phones are tolerable is:

$\left | w-0.4\right | \leq 9$

Report an Error

Example Question #2 : Absolute Value Inequalities

Solve for x: $|x-1|\le 5$

Possible Answers:

$x \le 6$

$x \ge 6$

x < 6

x>6

Correct answer:

$x \le 6$

Explanation:

Step 1: Separate the equation into two equations:

First Equation: $|x-1|\le 6$
Second Equation: $-(x-1)\ge -5$

Step 2: Solve the first equation

$x-1\le 5$
$x-1+1\le 5+1$
$x \le 6$

Step 3: Solve the second equation

$-(x+1)\ge -5$
$-x+1\ge -5$
$-x+1-1\ge -5-1$

$-x \ge -6$

$\rightarrow x \le 6$

The solution is $x\le 6$

Report an Error

Example Question #2 : Absolute Value Inequalities

Which of the following expresses the entire solution set of $\left | x-10\right |+ 3 < 12$ ?

Possible Answers:

1<x<19

x<1 and x>19

-5<x<19

x>19 and x< -5

Correct answer:

1<x<19

Explanation:

Before expanding the quantity within absolute value brackets, it is best to simplify the "actual values" in the problem. Thus $\left | x-10 \right |+3<12$ becomes:

$\left | x-10 \right |<9$

From there, note that the absolute value means that one of two things is true: x-10<9 or x-10>-9 . You can therefore solve for each possibility to get all possible solutions. Beginning with the first:

x-10<9 means that:

x<19

For the second:

x-10>-9 means that:

x>1

Note that the two solutions can be connected by putting the inequality signs in the same order:

1<x<19

Report an Error

View Tutors

Edem
Certified Tutor

University of Ghana, Bachelor, Mathematics. African Institute of Mathematical Science, Master's/Graduate, Mathematics.

View Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

View Tutors

Pankaj
Certified Tutor

University of Delhi, Electrical Engineer, Electrical Engineering. Columbia University in the City of New York, Master of Arts...

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Computer Science Tutors in Chicago, French Tutors in San Francisco-Bay Area, GRE Tutors in Dallas Fort Worth, English Tutors in Chicago, Calculus Tutors in Phoenix, Statistics Tutors in Seattle, MCAT Tutors in San Diego, MCAT Tutors in Houston, ACT Tutors in Dallas Fort Worth, Statistics Tutors in Atlanta

Popular Courses & Classes

GMAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Miami, GMAT Courses & Classes in San Diego, GRE Courses & Classes in Miami, GMAT Courses & Classes in Chicago, SAT Courses & Classes in Miami, Spanish Courses & Classes in Phoenix, ISEE Courses & Classes in New York City, ISEE Courses & Classes in Denver

Popular Test Prep

GRE Test Prep in Atlanta, LSAT Test Prep in Philadelphia, GMAT Test Prep in Chicago, ISEE Test Prep in New York City, GRE Test Prep in San Francisco-Bay Area, LSAT Test Prep in Seattle, GMAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Miami, ISEE Test Prep in Dallas Fort Worth, SSAT Test Prep in Houston

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

GRE Subject Test: Math : Absolute Value Inequalities

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

All GRE Subject Test: Math Resources

Example Questions

Example Question #232 : Gre Subject Test: Math

Example Question #1 : Absolute Value Inequalities

Example Question #1 : Absolute Value Inequalities

Example Question #234 : Gre Subject Test: Math

Example Question #2 : Absolute Value Inequalities

Example Question #1 : Absolute Value Inequalities

Example Question #1 : Absolute Value Inequalities

Example Question #3 : Absolute Value Inequalities

Example Question #2 : Absolute Value Inequalities

Example Question #2 : Absolute Value Inequalities

All GRE Subject Test: Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: