Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : How to solve absolute value equations

Study concepts, example questions & explanations for Algebra 1

Create An Account

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #41 : How To Solve Absolute Value Equations

Solve for .

$\left | x\right |+3=9$

Possible Answers:

$\pm6$

$\pm12$

Correct answer:

$\pm6$

Explanation:

To solve this problem we first need to isolate the variable on one side with all other constants on the other side.

$\left | x\right |+3=9$

To accomplish this perform the opposite opperation therefore subtract on both sides.

$\left | x\right |=6$

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will set up two equations to solve,

x=6 and -x=6 .

For the second equation divide both sides by to get x=-6 .

Therefore the solutions are,

$x=\pm6$ .

Report an Error

Example Question #42 : How To Solve Absolute Value Equations

Solve for .

$\left | x-8\right |=17$

Possible Answers:

-9, 25

$\pm9$

$\pm25$

Correct answer:

-9, 25

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve

x-8=17 and -(x-8)=17 .

For the first equation add to both sides to get x=25 .

For the second equation, by distributing the negative sign, we have: -x+8=17 .

Now subtract to both sides and divide both sides by to get x=-9 .

Therefore, the solutions are,

x=-9, 25 .

Report an Error

Example Question #43 : How To Solve Absolute Value Equations

Solve for .

$\left | x-10\right |=8$

Possible Answers:

2, 18

Correct answer:

2, 18

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve

Equation 1:

x-10=8

Add to both sides. x=18

Equation 2:

-(x-10)=8

By distributing the negative sign, we have: -x+10=8 Subtract to both sides and divide both sides by , we get x=2 . Remember, since is greater than and is negative, our answer is negative and we treat as a normal subtraction problem.

Therefore, the solutions are,

x=2, 18 .

Report an Error

Example Question #44 : How To Solve Absolute Value Equations

Solve for .

$5\left | x\right |=95$

Possible Answers:

$\pm19$

Correct answer:

$\pm19$

Explanation:

First we will need to isolate the variable on one side of the equation and all other constants on the other side.

$5\left | x\right |=95$

Divide both sides by .

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve.

Equation 1:

x=19

Equation 2:

-x=19

Divide on both sides to get x=-19 .

Therefore, the solutions are,

$x=\pm19$ .

Report an Error

Example Question #45 : How To Solve Absolute Value Equations

Solve for .

$\left | 3x\right |=78$

Possible Answers:

$\pm78$

$\pm26$

Correct answer:

$\pm26$

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve.

Equation 1:

3x=78

Divide on both sides. x=26 .

Equation 2:

-3x=78

Divide on both sides. x=-26 .

Therefore, the solutions are,

$x=\pm26$ .

Report an Error

Example Question #46 : How To Solve Absolute Value Equations

Solve for .

$\left | 4x+5\right |=37$

Possible Answers:

$\pm8$

8, -10.5

-10.5

$\pm10.5$

Correct answer:

8, -10.5

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve.

Equation 1: 4x+5=37

Subtract to both sides. Then divide to both sides. x=8

Equation 2: -(4x+5)=37

By distributing the negative sign, we have: -4x-5=37

Add to both sides and divide both sides by , we get x=-10.5 .

Therefore, the solutions are,

x=-10.5, 8 .

Report an Error

Example Question #47 : How To Solve Absolute Value Equations

Solve for .

$\left | \frac{x}{6} \right |=8$

Possible Answers:

$\pm1.5$

$\pm48$

1.5

Correct answer:

$\pm48$

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve.

Equation 1:

$\frac{x}{6} =8$

Multiply on both sides. x=48 .

Equation 2:

$\frac{-x}{6}=8$

Multiply on both sides and divide on both sides. x=-48 .

Therefore, the solutions are, $x=\pm48$ .

Report an Error

Example Question #48 : How To Solve Absolute Value Equations

Solve for .

$\left | \frac{x}{7}+3 \right |=9$

Possible Answers:

42, 84

42, -84

Correct answer:

42, -84

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve.

Equation1:

$\frac{x}{7}+3 =9$

Subtract on both sides and then multiply on both sides to get x=42 .

Equation2:

$-(\frac{x}{7}+3)=9$

By distributing the negative sign, we have: $-\frac{x}{7}-3=9$ . Add to both sides and multiply both sides by , we get x=-84 .

Therefore, the solutions are,

x=42, -84 .

Report an Error

Example Question #49 : How To Solve Absolute Value Equations

Solve.

$\left | 2x-3\right |-7=0$

Possible Answers:

No solution

$x=3\ \text{or}\ x=-5$

$x=-5\ \text{or}\ x=5$

$x=-2\ \text{or}\ x=5$

$x=-1\ \text{or}\ x=-5$

Correct answer:

$x=-2\ \text{or}\ x=5$

Explanation:

$\left | 2x-3\right |-7=0$

$\left | 2x-3\right |=7$

$(2x-3)=7\ \text{or} -(2x-3)=7$

$2x=7+3\ \text{or}\ 2x=-7+3$

$2x=10\ \text{or}\ 2x=-4$

$x=5\ \text{or}\ x=-2$

Report an Error

Example Question #50 : How To Solve Absolute Value Equations

Solve for :

$\left | x+7\right |=7$

Possible Answers:

Correct answer:

Explanation:

We define the absolute value of a number as that number's distance from on the number line. Given $\left | x+7\right |=7$ , we therefore must solve for two possibilities:

1.) x+7=7 , or

2.) x+7=-7

Solving #1, we get:

x+7=7

x=0

Solving #2, we get:

x+7=-7

x=-14

Consequently, the solution is x=0 or x=-14 .

Report an Error

View Algebra Tutors

Nate
Certified Tutor

University of Wisconsin-Oshkosh, non degree, Prepharmacy. University of Wisconsin-Madison, Pharmaceutical Chemist, Pharmacy.

View Algebra Tutors

Chelsea
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Physics. The University of Texas at Dallas, Master of Science, Bioinf...

View Algebra Tutors

Mariam
Certified Tutor

Yarmouk University, Bachelor of Science, Mathematics. Touro College, Master of Science, Teacher Education, Multiple Levels.

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GMAT Tutors in Miami, Spanish Tutors in Boston, Computer Science Tutors in San Diego, Physics Tutors in Washington DC, Statistics Tutors in Philadelphia, Reading Tutors in New York City, ISEE Tutors in Washington DC, Math Tutors in San Francisco-Bay Area, MCAT Tutors in Houston, Algebra Tutors in Houston

Popular Courses & Classes

SSAT Courses & Classes in Phoenix, ACT Courses & Classes in Atlanta, SSAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Seattle, Spanish Courses & Classes in Phoenix, ISEE Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Seattle, MCAT Courses & Classes in Atlanta, GRE Courses & Classes in New York City, ISEE Courses & Classes in Phoenix

Popular Test Prep

GMAT Test Prep in San Diego, GRE Test Prep in Dallas Fort Worth, SSAT Test Prep in Philadelphia, SAT Test Prep in Philadelphia, ISEE Test Prep in Chicago, ISEE Test Prep in San Francisco-Bay Area, ISEE Test Prep in Los Angeles, SAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Boston, SSAT Test Prep in Washington DC

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

Algebra 1 : How to solve absolute value equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #41 : How To Solve Absolute Value Equations

Example Question #42 : How To Solve Absolute Value Equations

Example Question #43 : How To Solve Absolute Value Equations

Example Question #44 : How To Solve Absolute Value Equations

Example Question #45 : How To Solve Absolute Value Equations

Example Question #46 : How To Solve Absolute Value Equations

Example Question #47 : How To Solve Absolute Value Equations

Example Question #48 : How To Solve Absolute Value Equations

Example Question #49 : How To Solve Absolute Value Equations

Example Question #50 : How To Solve Absolute Value Equations

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: