Call Now to Set Up Tutoring:

(888) 888-0446

Create an account to track your scores
and create your own practice tests:

Create an Account Create a Practice Test

All SAT Mathematics Resources

137 Practice Tests Question of the Day Flashcards Learn by Concept

Want to review SAT Mathematics but don’t feel like sitting for a whole test at the moment? Varsity Tutors has you covered with thousands of different SAT Mathematics flashcards! Our SAT Mathematics flashcards allow you to practice with as few or as many questions as you like. Get some studying in now with our numerous SAT Mathematics flashcards.

Flashcards: Understanding Absolute Values

Which of the following, if solved, would yield the set of all real numbers that are exactly 15 units away from -3?

$\left | x-15 \right |=3$

$\left | x-3 \right |=15$

$\left | x+3 \right |=15$

$\left | x+15 \right |=3$

Report an Error Copyright Notice

Flashcards: Understanding Absolute Values

Which of the following, if solved, would yield the set of all real numbers that are exactly 15 units away from -3?

Your answer:

$\left | x-15 \right |=3$

Your answer:

$\left | x-3 \right |=15$

Your answer:

$\left | x+15 \right |=3$

Correct answer:

$\left | x+3 \right |=15$

Explanation:

If you're looking for a number exactly units to either side of , you need an absolute value equation that gives you answers of -3+15=12 and -3-15=-18 .

One way forward is to simply solve each equation for using the two-case method, assuming first that the expression within the absolute value signs positive and then that it is negative and solving the resulting equation for each case.

If you do so, choice $\left | x+3 \right |=15$ becomes: x+3=15 , or x=12 and x+3=-15 , or x=-18 , which is correct.

Choice $\left | x-3 \right |=15$ becomes: x-3=15 , or x=18 , which doesn't work.

Choice $\left | x-15 \right |=3$ becomes: x-15=3 , or x=18 , which doesn't match.

Choice $\left | x+15 \right |=3$ becomes: x+15=3 , or x=-12 , which doesn't work.

You could also quickly solve this question if you remember the general way number line absolute value problems like this one work. Each one will be in the general form $\left | x-Center\, Value \right |=Distance$ , where the "Distance" referenced is the distance from the center value to one of the two values for .

So in this case the "center value" would be and the "distance" would be , yielding an equation of $\left | x+3 \right |=15$ .

Flashcards: Understanding Absolute Values

If is an integer, what is the value of such that $\left | -5x+7 \right |$ is minimized?

Report an Error Copyright Notice

Flashcards: Understanding Absolute Values

If is an integer, what is the value of such that $\left | -5x+7 \right |$ is minimized?

Your answer:

Correct answer:

Explanation:

Any time you have an absolute value equation and a question that is asking for the smallest possible value for the expression, remember that absolute value expressions can be zero but can never be less than 0. There are two ways to solve a problem like the one given. The first is by finding the value of such that the expression within the absolute value signs is zero and then finding the closest integer to that number. The second is by inspection (simply using brute force to find the value for x that will minimize the value given).

If you set -5x+7-5x=-7 , and that $x=\frac{7}{5}$ . Since $\frac{7}{5}=1.4$ , the closest integer value is x=1 , which will yield a value of $\left | -5+7 \right |=2$ .

The other way to approach this problem is by inspection, or through brute force. Try plugging in a few values for to see what happens.

If x=0 then the expression is $\left | -5(0)+7 \right |=7$

If x=1 , then the expression is $\left | -5(1)+7 \right |=2$ .

If x=2 then the expression becomes $\left | -5(2)+7 \right |=3$ .

Notice that the function decreases and then increases around x=1 , indicating that (for integer values, at least) x=1 will yield the smallest result for $\left | -5x+7 \right |$ .

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)

View Tutors

Samuel
Certified Tutor

Edinboro University of Pennsylvania, Bachelor of Science, Mathematics.

View Tutors

Bhakti
Certified Tutor

Stony Brook University, Bachelor of Science, Applied Mathematics. New York Institute of Technology, Doctor of Medicine, Preme...

View Tutors

Jordan
Certified Tutor

Marquette University, Bachelor of Science, Accounting and Finance.

Popular Subjects

LSAT Tutors in Atlanta, Calculus Tutors in San Francisco-Bay Area, Spanish Tutors in Miami, Calculus Tutors in Atlanta, French Tutors in Seattle, ACT Tutors in Chicago, Algebra Tutors in Houston, Statistics Tutors in San Diego, Computer Science Tutors in Dallas Fort Worth, Math Tutors in Seattle

Popular Courses & Classes

ACT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Atlanta, LSAT Courses & Classes in Chicago, GRE Courses & Classes in Miami, ACT Courses & Classes in Washington DC, SSAT Courses & Classes in Washington DC, SSAT Courses & Classes in Denver, SAT Courses & Classes in Denver, SSAT Courses & Classes in Boston

Popular Test Prep

LSAT Test Prep in New York City, LSAT Test Prep in Miami, ISEE Test Prep in Dallas Fort Worth, GRE Test Prep in Seattle, GRE Test Prep in Denver, ACT Test Prep in Dallas Fort Worth, SSAT Test Prep in Los Angeles, GMAT Test Prep in Seattle, GMAT Test Prep in Los Angeles, SAT Test Prep in Atlanta

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Create an account to track your scores
and create your own practice tests:

All SAT Mathematics Resources

Flashcards: Understanding Absolute Values

Flashcards: Understanding Absolute Values

Flashcards: Understanding Absolute Values

Flashcards: Understanding Absolute Values

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback:

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Create an account to track your scores and create your own practice tests:

All SAT Mathematics Resources

Flashcards: Understanding Absolute Values

Flashcards: Understanding Absolute Values

Flashcards: Understanding Absolute Values

Flashcards: Understanding Absolute Values

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Create an account to track your scores
and create your own practice tests: