We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Linear 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 #831 : Linear Equations

Solve for :

4x- 4 = 20

Possible Answers:

-6

Correct answer:

Explanation:

To get by itself, first add 4 to both sides of the equation:

4x - 4 = 20

4x = 24

Then, divide each side of the equation by 4:

4x=24

x = 6

Report an Error

Example Question #292 : How To Solve Two Step Equations

Solve for .

$5x^{2}=80$

Possible Answers:

$\frac{\sqrt{80}}{\sqrt{5}}$

$\sqrt{1.26}$

Correct answer:

Explanation:

Divide each side of the equation by 5.

$x^{2}=16$

Take the square root of each side of the equation.

x=4

Report an Error

Example Question #832 : Linear Equations

Solve for .

$\frac{4p}{5}+8 = 4$

Possible Answers:

None of the other answers

Correct answer:

Explanation:

Subtract 8 from each side of the equation.

$\frac{4p}{5}=-4$

Multiply each side of the equation by $\frac{5}{4}$ (the inverse of $\frac{4}{5}$ ).

$p=\frac{-4}{1}\times\frac{5}{4}=\frac{-20}{4}=-5$

Report an Error

Example Question #833 : Linear Equations

Solve for .

7(x+3)=70

Possible Answers:

$\frac{7}{6}$

Correct answer:

Explanation:

7(x+3)=70

Distribute 7 to the term in parentheses

7x+21=70

Subtract 21 from each side of the equation

7x=49

Divide each side by 7

x=7

Report an Error

Example Question #1 : How To Solve Absolute Value Equations

Solve the absolute value equation:

$\left | \frac{x-4}{3} \right| = \left | x +2 \right|$

Possible Answers:

$\small \varnothing$ (no solution)

$\small \left \{-5, -1 \right\}$

$\left \{-5 \right \}$

$\left \{-5, -\frac{1}{2} \right \}$

Correct answer:

$\left \{-5, -\frac{1}{2} \right \}$

Explanation:

An equation that equates two absolute value functions allows us to choose one of the absolute value functions and treat it as the constant. We then separate the equation into the "positive" version, $\tiny \small \frac{x-4}{3}=x+2$ , and the "negative" version, $\tiny \small \frac{x-4}{3} = -(x+2)$ . Solving each equation, we obtain the solutions, and $\tiny \tiny -\frac{1}{2}$ , respectively.

Report an Error

Example Question #1 : How To Solve Absolute Value Equations

Solve for x.

|x+3|=4

Possible Answers:

No solution

x = –3, 4

x = –7, 1

x = 4, 7

x = 1, 7

Correct answer:

x = –7, 1

Explanation:

First, split into two possible scenarios according to the absolute value.

x+3=4

x+3=-4

Looking at , we can solve for x by subtracting 3 from both sides, so that we get x = 1.

Looking at x+3=-4 , we can solve for x by subtracting 3 from both sides, so that we get x = –7.

So therefore, the solution is x = –7, 1.

Report an Error

Example Question #2 : How To Solve Absolute Value Equations

Find the solution to x for |x – 3| = 2.

Possible Answers:

2, 5

1, 4

1, 5

2, 4

Correct answer:

1, 5

Explanation:

|x – 3| = 2 means that it can be separated into x – 3 = 2 and x – 3 = –2.

So both x = 5 and x = 1 work.

x – 3 = 2 Add 3 to both sides to get x = 5

x – 3 = –2 Add 3 to both sides to get x = 1

Report an Error

Example Question #2 : How To Solve Absolute Value Equations

Solve for x:

$\small \left | x+2 \right |=12$

Possible Answers:

$\small x=-14$ or $\small x=10$

$\small x=-10$

$\small x=14$ or $\small x=-10$

$\small x=10$

Correct answer:

$\small x=-14$ or $\small x=10$

Explanation:

Because of the absolute value signs,

$\small x+2=12$ or $\small x+2=-12$

Subtract 2 from both sides of both equations:

$\small x+2-2=12-2$ or $\small x+2-2=-12-2$

$\small x=10$ or $\small x=-14$

Report an Error

Example Question #2 : How To Solve Absolute Value Equations

Solve for :

$|x-4|=\frac{5}{8}$

Possible Answers:

$x=4\frac{5}{8}, -4\frac{3}{8}$

$x=4\frac{5}{8}, -3\frac{5}{8}$

$x=4\frac{5}{8}, -3\frac{3}{8}$

$x=4\frac{3}{8}, -3\frac{3}{8}$

$x=4\frac{5}{8}$

Correct answer:

$x=4\frac{5}{8}, -3\frac{3}{8}$

Explanation:

$|x-4|=\frac{5}{8}$

There are two answers to this problem:

$x-4=\frac{5}{8}$

$x=\frac{5}{8}+4=4\frac{5}{8}$

and

$-(x-4)=\frac{5}{8}$

$4-x=\frac{5}{8}$

$-x=\frac{5}{8}-4=-3\frac{3}{8}$

$x=-3\frac{3}{8}$

Report an Error

Example Question #6 : How To Solve Absolute Value Equations

If x = 2 , evaluate $\left | -4x + 3\right | \left | 3x-14\right |$ .

Possible Answers:

220

Correct answer:

Explanation:

An absolute value expression differs from a normal expression only in its sign. Instead of being a positive or negative quantity, an absolute value represents a scalar distance from zero, so it does not have a sign. For example, $\left | -2\right |$ is the same as $\left | 2\right |$ because both represent a value 2 units away from zero. In this problem, $\left | -4x + 3\right |$ equals $\left | -5 \right |$ , or 5. $\left | 3x - 14\right |$ equals 8. The final answer is (5)(8) or 40.

Report an Error

View Algebra Tutors

Max
Certified Tutor

SHAHiDBEHESHTiUNiVERSiTY, Bachelor of Science, Mathematics. SHAHiDBEHESHTiUNiVERSiTY, Master of Science, Mathematics.

View Algebra Tutors

Christopher
Certified Tutor

Estrella Mountain Community College, Associate in Science, Science Technology. Arizona State University, Engineering, Compute...

View Algebra Tutors

Alison
Certified Tutor

Georgia Institute of Technology-Main Campus, Current Undergrad Student, Mechanical Engineering.

All Algebra 1 Resources

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

Popular Subjects

SSAT Tutors in Houston, ISEE Tutors in Washington DC, SAT Tutors in Seattle, Biology Tutors in Dallas Fort Worth, MCAT Tutors in Atlanta, Physics Tutors in Dallas Fort Worth, SSAT Tutors in Seattle, MCAT Tutors in New York City, Math Tutors in Chicago, Statistics Tutors in Miami

Popular Courses & Classes

GRE Courses & Classes in New York City, ACT Courses & Classes in San Diego, GMAT Courses & Classes in Seattle, MCAT Courses & Classes in Philadelphia, GRE Courses & Classes in Atlanta, GMAT Courses & Classes in Chicago, GRE Courses & Classes in Houston, Spanish Courses & Classes in Atlanta, GRE Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Chicago

Popular Test Prep

ISEE Test Prep in Atlanta, ACT Test Prep in San Diego, ACT Test Prep in Philadelphia, GRE Test Prep in Denver, GRE Test Prep in Washington DC, GRE Test Prep in Dallas Fort Worth, MCAT Test Prep in Denver, GMAT Test Prep in New York City, MCAT Test Prep in Boston, GRE Test Prep in Phoenix

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 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #831 : Linear Equations

Example Question #292 : How To Solve Two Step Equations

Example Question #832 : Linear Equations

Example Question #833 : Linear Equations

Example Question #1 : How To Solve Absolute Value Equations

Example Question #1 : How To Solve Absolute Value Equations

Example Question #2 : How To Solve Absolute Value Equations

Example Question #2 : How To Solve Absolute Value Equations

Example Question #2 : How To Solve Absolute Value Equations

Example Question #6 : 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: