Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Simplifying 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 #471 : Basic Single Variable Algebra

Simplify:

$\frac{25x^{2}y^{3}}{20x^{2}y^{6}}$

Possible Answers:

$\frac{5}{4y^{2}}$

$\frac{5y^{3}}{4}$

$\frac{5y^{3}}{4y^{6}}$

$\frac{5}{4y^{3}}$

$\frac{4y^{3}}{5}$

Correct answer:

$\frac{5}{4y^{3}}$

Explanation:

To simplify the equation you need to divide the numerator (top) and denominator (bottom), so:

The numerator can be factored to:

5*5*x*x*y*y*y

The denominator can be factored to:

4*5*x*x*y*y*y*y*y*y

$\frac{5*5*x*x*y*y*y}{4*5*x*x*y*y*y*y*y*y}$

After reducing, we will get

$\frac{5}{4*y*y*y} = \frac{5}{4y^{3}}$

Report an Error

Example Question #471 : Basic Single Variable Algebra

Simplify:

$\frac{4x^{2}}{2x}$

Possible Answers:

$\frac{4x}{2}$

Correct answer:

Explanation:

To simplify the equation you need to divide the numerator (top) and denominator (bottom), so:

The numerator can be factored to:

2*2*x*x

The denominator can be factored to:

2*x

$\frac{2*2*x*x}{2*x}$

After reducing, we will get

Report an Error

Example Question #2311 : Algebra Ii

Solve for : $\frac{x(x^3+3y)}{x+2} = 2x$

Possible Answers:

$y=-\frac{1}{3}x^3+\frac{2}{3}x+\frac{4}{3}$

$y=-\frac{4}{3}x^3+\frac{2}{3}x+\frac{4}{3}$

$y=\frac{1}{3}x^3+\frac{2}{3}x+\frac{4}{3}$

$y=-\frac{1}{3}x^3-\frac{2}{3}x-\frac{4}{3}$

$y=-\frac{1}{3}x^4+\frac{2}{3}x^2+\frac{4}{3}x$

Correct answer:

$y=-\frac{1}{3}x^3+\frac{2}{3}x+\frac{4}{3}$

Explanation:

Multiply x+2 on both sides in order to eliminate the denominator.

$\frac{x(x^3+3y)}{x+2} \cdot (x+2)= 2x\cdot (x+2)$

Simplify both sides.

x(x^3+3y) = 2x(x+2)

Use distribution to simplify both sides.

x^4+3xy = 2x^2+4x

Isolate the term with only the y-variable by subtracting x^4 on both sides.

x^4+3xy -x^4= 2x^2+4x-x^4

Simplify and reorder the right side by the order of power.

3xy = -x^4+2x^2+4x

Divide by on both sides.

$\frac{3xy}{3x} = \frac{-x^4+2x^2+4x}{3x}$

Simplify both sides.

The answer is: $y=-\frac{1}{3}x^3+\frac{2}{3}x+\frac{4}{3}$

Report an Error

Example Question #2314 : Algebra Ii

Simplify the equation: 6(2x-3)=-48

Possible Answers:

$-\frac{11}{2}$

$-\frac{2}{11}$

$-\frac{3}{2}$

$-\frac{5}{2}$

$-\frac{2}{5}$

Correct answer:

$-\frac{5}{2}$

Explanation:

In order to simplify and solve this equation, divide by six on both sides.

$\frac{6(2x-3)}{6}=\frac{-48}{6}$

Simplify both sides.

2x-3=-8

Add three on both sides.

2x-3+3=-8+3

Simplify both sides.

2x=-5

Divide both sides by two.

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

The answer is: $x=-\frac{5}{2}$

Report an Error

Example Question #2315 : Algebra Ii

Simplify the following equation: 3x+9 = -57

Possible Answers:

Correct answer:

Explanation:

Subtract nine from both sides.

3x+9 -9= -57-9

3x=-66

Divide both sides.

$\frac{3x}{3}=\frac{-66}{3}$

x=-22

The answer is:

Report an Error

Example Question #2312 : Algebra Ii

Simplify the equation: 2(3x-2) -38= 0

Possible Answers:

$\frac{17}{3}$

$-\frac{17}{3}$

$\frac{1}{7}$

Correct answer:

Explanation:

Add 38 on both sides.

2(3x-2) -38+38= 0+38

2(3x-2)=38

Divide by two on both sides.

$\frac{2(3x-2) }{2}= \frac{38}{2}$

The equation becomes:

3x-2 = 19

Add two on both sides.

3x-2 +2= 19+2

3x=21

Divide by three on both sides.

$\frac{3x}{3}=\frac{21}{3}$

The answer is:

Report an Error

Example Question #2317 : Algebra Ii

Simplify the equation: $(\frac{2}{5}x)^2+\frac{1}{2}x-\frac{2}{5}x-8$

Possible Answers:

$\frac{4}{25}x^2+\frac{1}{10}x-8$

None of the other answers.

$\frac{4}{25}x+\frac{1}{10}x-8$

$\frac{2}{5}x^2+\frac{1}{10}x-8$

$\frac{4}{25}x^2-\frac{3}{7}x-8$

Correct answer:

$\frac{4}{25}x^2+\frac{1}{10}x-8$

Explanation:

$(\frac{2}{5}x)^2+\frac{1}{2}x-\frac{2}{5}x-8$

Start by squaring everything within the parentheses:

$\frac{4}{25}x^2+\frac{1}{2}x-\frac{2}{5}x-8$

Now combine the fractions of degree 1 by finding a common denominator:

$\frac{4}{25}x^2+\frac{5}{5}*\frac{1}{2}x-\frac{2}{2}*\frac{2}{5}x-8$

$\frac{4}{25}x^2+\frac{5}{10}x-\frac{4}{10}x-8\rightarrow \boldsymbol{\frac{4}{25}x^2+\frac{1}{10}x-8}$

Report an Error

Example Question #11 : Simplifying Equations

Simplify this expression:

$(4x^{4}-x^{2})+(x^2+5x^4)$

Possible Answers:

$9x^{4}-2x^{2}$

3x^2-1

$x^{4}+x^{2}$

$9x^{4}$

$-x^{4}-x^{2}$

Correct answer:

$9x^{4}$

Explanation:

Drop the parentheses and combine like terms.

$5x^{4}+4x^{4}=9x^{4}$

and

$-x^{2}+x^{2}=0$

Report an Error

Example Question #2321 : Algebra Ii

Simplify the expression by combining like terms.

Simplify:

5x^2+15x+18 = 6x^2-8x+9

Possible Answers:

x^2+23x+9 = 0

-x^2-23x+27 = 0

5x^2-23x-9 = 6x^2

11x^2-23x-9 = 0

x^2-23x-9 = 0

Correct answer:

x^2-23x-9 = 0

Explanation:

The original equation:

5x^2+15x+18 = 6x^2-8x+9

Now move all terms to one side, in this example, we will use the right side, but either side will work.

0 = 6x^2 - 8x + 9 -5x^2 -15x-18

As you can see, we subtracted the terms on the left from both sides, effectively moving them to the other side.

Regrouping the terms so that "like terms" are together. Like terms are defined by having the same power of x.

0= (6x^2-5x^2)+(-8x-15x)+(9-18)

Now, we add any terms that have like powers of x.

x^2-23x-9 = 0

Now that all terms have been combined, we are finished. The equation is simplified.

Report an Error

View Algebra 2 Tutors

Shivansh
Certified Tutor

University of British Columbia, Bachelor, Math major and data science minor .

View Algebra 2 Tutors

Renetta
Certified Tutor

Langston University, Bachelor of Science, Education of Individuals in Elementary Special Education Programs.

View Algebra 2 Tutors

Anjali
Certified Tutor

Delhi University, Bachelor of Science, Physics. Kumuan University, Master of Science, Physics.

All Algebra II Resources

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

Popular Subjects

English Tutors in Chicago, Biology Tutors in Dallas Fort Worth, SAT Tutors in Denver, MCAT Tutors in Seattle, SAT Tutors in Houston, SAT Tutors in Boston, English Tutors in San Francisco-Bay Area, GRE Tutors in Los Angeles, Math Tutors in San Diego, ISEE Tutors in Atlanta

Popular Courses & Classes

LSAT Courses & Classes in Washington DC, Spanish Courses & Classes in New York City, ISEE Courses & Classes in Phoenix, GMAT Courses & Classes in Philadelphia, MCAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Chicago, SSAT Courses & Classes in Phoenix, GMAT Courses & Classes in Washington DC, ACT Courses & Classes in Denver, SAT Courses & Classes in Washington DC

Popular Test Prep

SSAT Test Prep in Chicago, MCAT Test Prep in Chicago, ACT Test Prep in San Diego, SSAT Test Prep in Washington DC, SSAT Test Prep in Miami, ACT Test Prep in New York City, GMAT Test Prep in Philadelphia, ACT Test Prep in Atlanta, GMAT Test Prep in Seattle, MCAT Test Prep in New York City

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 : Simplifying Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #471 : Basic Single Variable Algebra

Example Question #471 : Basic Single Variable Algebra

Example Question #2311 : Algebra Ii

Example Question #2314 : Algebra Ii

Example Question #2315 : Algebra Ii

Example Question #2312 : Algebra Ii

Example Question #2317 : Algebra Ii

Example Question #11 : Simplifying Equations

Example Question #2321 : Algebra Ii

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: