We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Algebra 1

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 #16 : How To Solve Absolute Value Equations

Solve for :

| 2x + 15 | = -77

Possible Answers:

x = 31

$x \in \left \{ 31,46\right \}$

x = 31

There is no solution.

$x \in \left \{ -31,46\right \}$

$x \in \left \{ -46, 31\right \}$

Correct answer:

There is no solution.

Explanation:

The absolute value of a number can never be a negative number. Therefore, no value of can make | -3x - 15 | = -42 a true statement.

Report an Error

Example Question #12 : How To Solve Absolute Value Equations

Solve for .

|x+3|=1

Possible Answers:

x=-4

$x=0\ \text{or}\ x=-3$

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

$x=0\ \text{or}\ x=3$

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

Correct answer:

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

Explanation:

|x+3|=1

The equation involves an absolute value. First, we need to rewrite the equation with no absolute value.

$x+3=\pm 1$

We can split this equation into two possible equations.

Equation 1: x+3 =1

Equation 2: x+3 =-1

With two equations, there are two values for . Let's start with Equation 1.

x+3 =1

Subtract from both sides.

x+3-3=1-3

x=-2

That's the first value for . To get the second value for , we need to repeat the steps, but with Equation 2.

x+3 =-1

x+3-3=-1-3

x=-4

Report an Error

Example Question #851 : Algebra 1

Solve for :

$\left | 2x-7 \right | -15 = -6$

Possible Answers:

$x=-8\textup{ or }x=8$

$x=-1\ \textup{or }x=8$

$x=-8\ \textup{or }x=1$

x=8

$x=-1\textup{ or }x=1$

Correct answer:

$x=-1\ \textup{or }x=8$

Explanation:

First, isolate the absolute value expression on one side.

$\left | 2x-7 \right | -15 = -6$

$\left | 2x-7 \right | -15 + 15= -6 + 15$

$\left | 2x-7 \right | =9$

Rewrite this as the compound statement:

2x-7 =-9 or 2x-7 =9

Solve each equation separately:

2x-7 =-9

2x-7+ 7 =-9 + 7

2x = -2

$2x\div 2 = -2 \div 2$

x=-1

2x-7 =9

2x-7+ 7 =9 + 7

2x = 16

$2x\div 2 = 16 \div 2$

x=8

Report an Error

Example Question #18 : How To Solve Absolute Value Equations

Solve for :

$\left | 2x +1 \right |=7$

Possible Answers:

x=3, -3

x=4, -3

x=-4, 3

$x=\pm4$

Correct answer:

x=-4, 3

Explanation:

Absolute value is a function that turns whatever is inside of it positive. This means that what's inside the function, 2x+1 , might be 7, or it could have also been -7. We have to solve for both situations.

a. 2x+1=7 subtract 1 from both sides

2x=6 divide both sides by 2

x=3

b. 2x+1=-7 subtract 1 from both sides

2x=-8 divide both sides by 2

x=-4

Report an Error

Example Question #21 : How To Solve Absolute Value Equations

$3(x+1)^2=\left | x+1\right |. \textup{Which is not a solution?}$

Possible Answers:

$-\frac{5}{3}$

$\textup{None of the above.}$

$-\frac{2}{3}$

$-\frac{4}{3}$

Correct answer:

$-\frac{5}{3}$

Explanation:

$\\ \textup{We get rid of the absolute value by solving the two equations }\\3(x+1)^2=x+1\\\textup{and}\\3(x+1)^2=-(x+1)\\\textup{If } x\neq1\textup{ we can divide in both equations the two sides by }\\ x+1 \textup{ and obtain }\\ 3(x+1)=1 \\\textup{ and }}\\ 3(x+1)=-1 \\\textup{ which give}}\\ \textup{the solutions } x=-\frac{2}{3} \textup{ and } x=-\frac{4}{3}.$

$\textup{If } x=-1, \textup{both sides are equal to 0, so } -1 \textup{ is another solution.}$

Report an Error

Example Question #22 : How To Solve Absolute Value Equations

Solve for all possible values of .

$\left |3x-2 \right | = -4$

Possible Answers:

x=-2,x=2/3

x=3,x=-2

x=2/3,x=-3

x=2,x=-3

x=-2/3, x=2

Correct answer:

x=-2/3, x=2

Explanation:

$\left |3x-2 \right |=-4$

First, ignore absolute value signs and solve for x.

3x-2=-4

3x=-2

x=-2/3

Now, for the other solution, ignore absolute value signs and change the sign of the right side of the equation. Solve for x.

3x-2=4

3x=6

x=2

Report an Error

Example Question #23 : How To Solve Absolute Value Equations

Solve for all values of .

$\left | 4x\right |-2=10$

Possible Answers:

x=3,x=2

x=-2,x=3

x=2,x=-2

x=3,x=-3

x=0,x=3

Correct answer:

x=3,x=-3

Explanation:

First, make sure to have the absolute value part of the equation by itself on the left side.

$\left | 4x\right |-2=10$

$\left | 4x\right |=12$

Now solve for both x values.

4x=12

x=3

Change the side of the right hand side to find the other value of x.

4x=-12

x=-3

Report an Error

Example Question #24 : How To Solve Absolute Value Equations

Solve for .

$\left | 2x-3\right | +2=5$

Possible Answers:

x = 0,3

x = 0, -3

x = 3, -3

x = 1, -3

x = 0, 1

Correct answer:

x = 0,3

Explanation:

The question is asking for the value of . To isolate , we must first isolate the absolute value expression.

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

The absolute value bars give a positive value to the result of the expression within. This means the real value of the inner expression could be positive or negative. To find the two values of , create the two possible equations.

2x-3=3 $\boldsymbol{\mathbf{OR}}$ 2x-3=-3

Balance the equations to find .

2x-3=3

2x=6

x=3

2x-3=-3

2x=0

x=0

Therefore, x= 0 and x=3

Also written as x= 0,3 .

Report an Error

Example Question #24 : How To Solve Absolute Value Equations

Solve for .

$\left | x\right |=10$

Possible Answers:

$\pm1$

$\pm10$

Correct answer:

$\pm10$

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

x=10

-x=10

Divide both sides by , we get x=-10 .

Final answer is $\pm10$ .

Report an Error

Example Question #25 : How To Solve Absolute Value Equations

Solve for .

$\left | x+5\right |=2$

Possible Answers:

-3, -7

3, 7

Correct answer:

-3, -7

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

x+5=2

Subtract both sides by , we get x=-3 .

-(x+5)=2

Distribute the negative sign to get -x-5=2 .

Add both sides by and divide both sides by to get x=-7 .

Final answer is -3, -7 .

Report an Error

View Algebra Tutors

Shakeel
Certified Tutor

View Algebra Tutors

Andrew
Certified Tutor

University of Wisconsin-Stevens Point, Bachelor of Science, Mathematics. University of Wisconsin-Oshkosh, Master of Science, ...

View Algebra Tutors

John
Certified Tutor

Northeastern University, Bachelors, Chemistry. Northeastern University, Masters, Chemistry.

All Algebra 1 Resources

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

Popular Subjects

Statistics Tutors in Chicago, Chemistry Tutors in New York City, Biology Tutors in Chicago, ACT Tutors in Chicago, Physics Tutors in New York City, MCAT Tutors in Seattle, Spanish Tutors in Miami, MCAT Tutors in Washington DC, ACT Tutors in Houston, SAT Tutors in Phoenix

Popular Courses & Classes

LSAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Denver, LSAT Courses & Classes in Chicago, SAT Courses & Classes in Boston, GMAT Courses & Classes in Houston, Spanish Courses & Classes in Miami, LSAT Courses & Classes in Phoenix, GMAT Courses & Classes in New York City, Spanish Courses & Classes in Phoenix

Popular Test Prep

GRE Test Prep in Washington DC, GMAT Test Prep in Miami, GMAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Chicago, SSAT Test Prep in Houston, MCAT Test Prep in Boston, SAT Test Prep in San Diego, LSAT Test Prep in Chicago, GRE Test Prep in Denver, GRE 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

Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #16 : How To Solve Absolute Value Equations

Example Question #12 : How To Solve Absolute Value Equations

Example Question #851 : Algebra 1

Example Question #18 : How To Solve Absolute Value Equations

Example Question #21 : How To Solve Absolute Value Equations

Example Question #22 : How To Solve Absolute Value Equations

Example Question #23 : How To Solve Absolute Value Equations

Example Question #24 : How To Solve Absolute Value Equations

Example Question #24 : How To Solve Absolute Value Equations

Example Question #25 : 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: