Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: High School - Algebra : High School: Algebra

Study concepts, example questions & explanations for Common Core: High School - Algebra

Create An Account

All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #12 : Reasoning With Equations & Inequalities

Solve for .

$1-\sqrt{x+1}=5$

Possible Answers:

x=4

x=16

x=24

x=5

x=15

Correct answer:

x=15

Explanation:

To solve for , first subtract one from both sides.

$1-\sqrt{x+1}=5$

____________________

$-\sqrt{x+1}=4$

From here, divide both sides by negative one.

$-\frac{\sqrt{x+1}}{-1}=\frac{4}{-1}$

$\sqrt{x+1}=-4$

Next, square both sides to cancel the square root sign on the left-hand side.

$(\sqrt{x+1})^2=(-4)^2$

x+1=16

Now, subtract one from both sides to solve for .

x+1=16

____________

x=15

Lastly, check for extraneous solutions by substituting the value found for into the original equation.

$1-\sqrt{x+1}=5$

$\\1-\sqrt{15+1}=5 \\1-\sqrt{16}=5 \\1-\pm4=5$

Thus, the answer is verified.

Report an Error

Example Question #1 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Solve for .

$\frac{1}{x}-2=10$

Possible Answers:

$x=-\frac{1}{12}$

x=12

$x=\frac{1}{12}$

x=-12

$x=\frac{1}{8}$

Correct answer:

$x=\frac{1}{12}$

Explanation:

To solve for , add two to both sides of the equation.

$\frac{1}{x}-2=10$

______________

$\frac{1}{x}=12$

Now, multiply by on both sides. This will move the variable from the denominator on one side to the numerator of the other side.

$x\cdot \frac{1}{x}=12\cdot x$

1=12x

Lastly, divide both sides by twelve.

$\frac{1}{12}=\frac{12x}{12}$

The twelve in the numerator and the twelve in the denominator cancel out thus, solving for .

$\frac{1}{12}=x$

Report an Error

Example Question #2 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Solve for .

$\sqrt{x}+4=3$

Possible Answers:

x=1

x=2

x=-1

x=3

x=5

Correct answer:

x=1

Explanation:

To solve for , first subtract four from both sides so all constants are on one side.

$\sqrt{x}+4=3$

_____________

$\sqrt{x}=-1$

Now, square both sides to cancel the square root sign on the left-hand side.

$(\sqrt{x})^2=(-1)^2$

x=1

Recall that when a negative number is squared the result is always a positive value.

From here, check for extraneous solutions by substituting in the value found for .

$\\\sqrt{x}+4=3 \\\sqrt{1}+4=3 \\\pm1+4=3 \\-1+4=3$

Since the square root of a value results in a positive and a negative value, our solution is verified.

Report an Error

Example Question #1 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Solve for .

$\sqrt{\frac{x}{2}}=6$

Possible Answers:

x=36

x=6

x=72

x=-72

x=24

Correct answer:

x=72

Explanation:

To solve for start by squaring both sides to eliminate the square root sign.

$\left( \sqrt{\frac{x}{2}}\right)^2=(6)^2$

$\frac{x}{2}=36$

From here multiply both sides by two. On the left-hand side, the two in the numerator will cancel out the two in the denominator.

$2\cdot \frac{x}{2}=36\cdot 2$

x=72

From here, check for extraneous solutions by substituting in the value found for into the original equation.

$\sqrt{\frac{x}{2}}=6$

$\sqrt{\frac{72}{2}}=6$

$\sqrt{36}=6$

$\pm6=6$

Thus, the solution is verified.

Report an Error

Example Question #2 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Solve for .

$\frac{3}{x}-2=5$

Possible Answers:

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

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

x=21

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

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

Correct answer:

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

Explanation:

To solve for , first add two to both sides.

$\frac{3}{x}-2=5$

____________

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

From here, multiply both sides by .

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

3=7x

Now divide by seven to solve for .

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

The seven in the numerator and seven in the denominator cancel out, thus solving for .

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

Report an Error

Example Question #2 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Solve for .

$\sqrt{5-x}=2$

Possible Answers:

x=2

x=-2

x=-1

x=1

x=0

Correct answer:

x=1

Explanation:

To solve for , first square both sides of the equation. Squaring a square root sign will cancel them out.

$(\sqrt{5-x})^2=(2)^2$

5-x=4

Now, subtract five from both sides to get all constants on one side of the equation while all variables are on the other side of the equation.

5-x=4

_____________

-x=-1

From here, divide by negative one on both sides.

$\frac{-x}{-1}=\frac{-1}{-1}$

x=1

Lastly, check for extraneous solutions by substituting in the value found for into the original equation.

$\\\sqrt{5-1}=2 \\\sqrt{4}=2 \\\pm2=2$

Thus, the solution is verified.

Report an Error

Example Question #8 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Solve for .

$\frac{x}{2}=8$

Possible Answers:

x=4

x=6

x=16

x=8

x=2

Correct answer:

x=16

Explanation:

To solve for , simply multiply both sides of the equation by two.

$\frac{x}{2}=8$

$2\cdot \frac{x}{2}=8\cdot 2$

The two in the numerator cancels the two in the denominator, thus solving for .

x=16

Report an Error

Example Question #9 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Solve for .

$2\sqrt{x}=14$

Possible Answers:

x=7

x=14

x=49

x=-14

x=-49

Correct answer:

x=49

Explanation:

To solve for , first divide by two.

$2\sqrt{x}=14$

$\frac{2\sqrt{x}}{2}=\frac{14}{2}$

The two in the denominator cancels the two in the numerator.

$\sqrt{x}=7$

From here, square both sides of the equation. Squaring a square root cancels it out.

$(\sqrt{x})^2=(7)^2$

x=49

To check for extraneous solutions, simply substitute into the original equation the value found for .

$2\sqrt{x}=14$

$\\2\sqrt{49}=14 \\2\cdot \pm 7=14 \\2(7)=14 \\2(-7)=-14\neq 14$

Report an Error

Example Question #10 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Solve for .

x^2-3=13

Possible Answers:

$x=\pm16$

x=16

x=4

x=-4

$x=\pm4$

Correct answer:

$x=\pm4$

Explanation:

To solve for , add three to both sides of the equation.

x^2-3=13

______________

x^2=16

From here, take the square root of both sides. Taking the square root of a squared term eliminates the square.

$\sqrt{x^2}=\sqrt{16}$

$x=\pm4$

Next, check for extraneous solutions. Substitute each potential solution into the original equation to verify if it results in a legal solution.

x^2-3=13

Substituting in positive four.

$\\4^2-3=13 \\16-3=13 \\13=13$

Substituting in negative four.

$\\(-4)^2-3=13 \\16-3=13 \\13=13$

Therefore, both answers are verified solutions.

Report an Error

Example Question #21 : Reasoning With Equations & Inequalities

Solve for .

$\sqrt{2-x}=7+3$

Possible Answers:

x=-102

x=102

x=-98

x=98

x=-100

Correct answer:

x=-98

Explanation:

To solve for , combine the like terms on the right-hand side.

$\sqrt{2-x}=7+3$

$\sqrt{2-x}=10$

From here, square both sides of the equation. Squaring a square root sign cancels it.

$(\sqrt{2-x})^2=(10)^2$

2-x=100

Now, subtract two from both sides so that all constants are on one side and all variables are on the other side.

2-x=100

_________________

-x=98

Next, divide both sides by negative one.

$\frac{-x}{-1}=\frac{98}{-1}$

x=-98

Lastly, check for extraneous solutions by substituting in the value found to into the original equation.

$\sqrt{2-x}=7+3$

$\\\sqrt{2--98}=7+3 \\\sqrt{100}=10 \\\pm10=10$

Therefore, the solution is verified.

Report an Error

View Tutors

Deenese
Certified Tutor

The University of Texas of the Permian Basin, Bachelor of Science, Biology, General.

View Tutors

Antonio
Certified Tutor

University of Murcia, Spain, Bachelor in Arts, Philosophy.

View Tutors

Jessica
Certified Tutor

University of Georgia, Bachelor in Business Administration, Business Administration and Management. Saint Louis University-Ma...

All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SSAT Tutors in Boston, ISEE Tutors in Los Angeles, GRE Tutors in San Francisco-Bay Area, ACT Tutors in Phoenix, French Tutors in Denver, Calculus Tutors in Denver, English Tutors in Miami, Biology Tutors in Phoenix, Statistics Tutors in Dallas Fort Worth, SSAT Tutors in Los Angeles

Popular Courses & Classes

MCAT Courses & Classes in Miami, SSAT Courses & Classes in San Diego, LSAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Atlanta, GRE Courses & Classes in Boston, ACT Courses & Classes in Houston, SSAT Courses & Classes in Washington DC, GMAT Courses & Classes in Chicago, Spanish Courses & Classes in Miami, MCAT Courses & Classes in Chicago

Popular Test Prep

GRE Test Prep in San Diego, LSAT Test Prep in Washington DC, GRE Test Prep in Dallas Fort Worth, SSAT Test Prep in Seattle, ACT Test Prep in Washington DC, LSAT Test Prep in Philadelphia, SAT Test Prep in San Diego, ISEE Test Prep in New York City, SSAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Seattle

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

Common Core: High School - Algebra : High School: Algebra

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #12 : Reasoning With Equations & Inequalities

Example Question #1 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Example Question #2 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Example Question #1 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Example Question #2 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Example Question #2 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Example Question #8 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Example Question #9 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Example Question #10 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Example Question #21 : Reasoning With Equations & Inequalities

All Common Core: High School - Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: