Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Solving Absolute Value Equations

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #3 : Absolute Value Inequalities

Solve the inequality.

$\small \left | x+2 \right |>5$

Possible Answers:

$\small x<-3\ or\ x>7$

$\small x<-7\ or\ x>3$

$\small -3<x<7$

$\small -7<x<3$

Correct answer:

$\small x<-7\ or\ x>3$

Explanation:

$\small \left | x+2 \right |>5$

Remove the absolute value by setting the term equal to either $\small 5$ or $\small -5$ . Remember to flip the inequality for the negative term!

$\small x+2>5\ or\ x+2<-5$

Solve each scenario independently by subtracting $\small 2$ from both sides.

$\small x+2-2>5-2\ or\ x+2-2<-5-2$

$\small x>3\ or\ x<-7$

Report an Error

Example Question #4 : Absolute Value Inequalities

Solve for :

| 4y + 7 | > -5

Possible Answers:

$(-\infty , -3) \cup (3, \infty )$

$\left(-\infty , -\frac{1}{2}\right) \cup \left (3, \infty \right)$

$\left(-\infty , -\frac{1}{2}\right) \cup \left ( \frac{1}{2}, \infty \right)$

$(-\infty , \infty )$

$(-\infty , -3) \cup \left ( \frac{1}{2}, \infty \right)$

Correct answer:

$(-\infty , \infty )$

Explanation:

The absolute value of any number is nonnegative, so | 4y + 7 | must always be greater than . Therefore, any value of makes this a true statement.

Report an Error

Example Question #4801 : Algebra Ii

Solve for .

$x+5=\left | 7\right |$

Possible Answers:

2, -12

Correct answer:

2, -12

Explanation:

When solving for absolute values, remember there's an equation for positive value and another equation for negative value.

x+5=7, x+5=-7 . S

ubtract on both sides of all equations.

x=2, x=-12

Report an Error

Example Question #12 : Solving Absolute Value Equations

Solve for .

$x-6=\left | 2\right |$

Possible Answers:

-4, -8

-2, -6

4, 8

Correct answer:

4, 8

Explanation:

When solving for absolute values, remember there's an equation for positive value and another equation for negative value.

x-6=2, x-6=-2

Add to both sides of both equations.

x=4, x=8

Report an Error

Example Question #12 : Solving Absolute Value Equations

Solve for .

$\frac{x}{5}=\left | 3\right |$

Possible Answers:

-5, 5

15, -15

Correct answer:

15, -15

Explanation:

When solving for absolute values, remember there's an equation for positive value and another equation for negative value.

$\frac{x}{5}=3, \frac{x}{5}=-3$

Multiply both sides by for both equations.

x=15, x=-15

Report an Error

Example Question #13 : Solving Absolute Value Equations

Solve for .

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

Possible Answers:

$-\frac{3}{7}$

$\pm \frac{7}{3}$

$\frac{3}{7}$

$\pm \frac{3}{7}$

$\frac{7}{3}$

Correct answer:

$\pm \frac{3}{7}$

Explanation:

When solving for absolute values, remember there's an equation for positive value and another equation for negative value.

7x=3, 7x=-3

Divide both sides by for both equations.

$x=\pm \frac{3}{7}$

Report an Error

Example Question #14 : Solving Absolute Value Equations

Solve:

$\left | 2x-1 \right |=13$

Possible Answers:

x=7, 6

x=-6

x=7,-6

x=7

x=-7,-6

Correct answer:

x=7,-6

Explanation:

To solve absolute value equations, you have to set up the equation two different ways to account for two answers.

The first is how you see it:

2x-1=13 .

The second is by making the answer negative:

2x-1=-13 .

Next solve each one for x. The first equation yields x to be 7. The second one gives you x=-6. Those are your two answers.

Report an Error

Example Question #15 : Solving Absolute Value Equations

Solve for :

$\left | x-5\right |+8<3$

Possible Answers:

$x<-6 \and\ x>16$

$x<0 \and\ x>10$

No solution

x<0

Correct answer:

No solution

Explanation:

Given

$\left | x-5\right |+8<3$

first subtract 8 from both sides to get on the right.

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

Based upon what we know about absolute value functions, it is impossible for an absolute value to be negative. So it is also impossible for an absolute value to be less than a negative number, which in this case is (-5) .

The only answer can be No Solution.

Report an Error

Example Question #12 : Absolute Value

Solve for :

$2 \left | 3x-1 \right | = 10$

Possible Answers:

1.5; -1.5

2; -2

2; 1.5

$2; -\frac{4}{3}$

1;0

Correct answer:

$2; -\frac{4}{3}$

Explanation:

Solve using inverse opperations:

$2 \left | 3x-1 \right | = 10$

Divide both sides by 2.

|3x - 1 | = 5

Because the absolute value function always makes whatever is inside positive, this gives us two solutions. 3x - 1 could be either or , so we'll solve for both:

3 x - 1 = 5

3x = 6

x = 2

3x - 1 = -5

3x = -4

$x = \frac{ -4}{3}$

Report an Error

Example Question #12 : Absolute Value

Solve for :

|2x - 7 | - 4 = 9

Possible Answers:

-1; 1

10; -10

10; 1

10; -3

-3; 1

Correct answer:

10; -3

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

|2x - 7 | - 4 = 9

First add 4 to both sides

|2x - 7 | = 13

The absolute value function makes whatever is inside positive, which means that there are two possible solutions. 2x - 7 could either be or
so we'll solve for both

2x - 7 = 13

2 x = 20

x = 10

2 x - 7 = -13

2x = -6

x = -3

Report an Error

View Algebra 2 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 2 Tutors

Ataul
Certified Tutor

Temple University, Bachelor of Science, Financial Planning.

View Algebra 2 Tutors

Mariam
Certified Tutor

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

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Computer Science Tutors in Chicago, Algebra Tutors in Denver, ISEE Tutors in Washington DC, Math Tutors in Chicago, Chemistry Tutors in Phoenix, Biology Tutors in Boston, Reading Tutors in Miami, Reading Tutors in Seattle, Math Tutors in Miami, Algebra Tutors in Washington DC

Popular Courses & Classes

GMAT Courses & Classes in Chicago, GRE Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Seattle, ACT Courses & Classes in Philadelphia, ACT Courses & Classes in Los Angeles, MCAT Courses & Classes in Boston, MCAT Courses & Classes in Seattle, SSAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in New York City, SSAT Courses & Classes in Washington DC

Popular Test Prep

GMAT Test Prep in Denver, GRE Test Prep in Denver, GRE Test Prep in Seattle, ACT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Phoenix, ISEE Test Prep in Denver, ISEE Test Prep in Philadelphia, SAT Test Prep in Atlanta, ACT Test Prep in Philadelphia, LSAT Test Prep in San Francisco-Bay Area

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 II : Solving Absolute Value Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #3 : Absolute Value Inequalities

Example Question #4 : Absolute Value Inequalities

Example Question #4801 : Algebra Ii

Example Question #12 : Solving Absolute Value Equations

Example Question #12 : Solving Absolute Value Equations

Example Question #13 : Solving Absolute Value Equations

Example Question #14 : Solving Absolute Value Equations

Example Question #15 : Solving Absolute Value Equations

Example Question #12 : Absolute Value

Example Question #12 : Absolute Value

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: