Call Now to Set Up Tutoring:

(888) 888-0446

Pre-Algebra : Algebraic Equations

Study concepts, example questions & explanations for Pre-Algebra

Create An Account

All Pre-Algebra Resources

11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #4 : Two Step Equations With Fractions

Solve for :

$1\frac{1}{3}x+7\frac{1}{3}=15\frac{1}{3}$

Possible Answers:

$6\frac{1}{3}$

$6\frac{2}{3}$

Correct answer:

Explanation:

Explanation:

The goal is to isolate the variable to one side.

$1\frac{1}{3}x+7\frac{1}{3}=15\frac{1}{3}$

First, convert the mixed numbers to improper fractions:

$\frac{4}{3}x+\frac{22}{3}=\frac{46}{3}$

Subtract $\frac{22}{3}$ from both sides:

$\frac{4}{3}x+\frac{22}{3}-\frac{22}{3}=\frac{46}{3}-\frac{22}{3}$

$\frac{4}{3}x=\frac{24}{3}$

Multiply each side by the reciprocal of $\frac{3}{4}$ :

$\frac{3}{4}*\frac{4}{3}x=\frac{24}{3}*\frac{3}{4}$

x=6

Report an Error

Example Question #5 : Two Step Equations With Fractions

Solve for ""

$\frac{1}{2}x -8=4x-1$

Possible Answers:

x=5

x=4

x=-2

x=2

x=-3

Correct answer:

x=-2

Explanation:

1.) Add 8 to both sides, removing the "". It now reads $\frac{1}{2}x=4x+7$

2.) Multiply both sides by 2, removing the $\frac{1}{2}$ . It now reads x=8x+14

3.) Subtract from both sides, removing the "". It now reads -7x=14

4.) Divide both sides by "", resulting in x=-2

Report an Error

Example Question #11 : Two Step Equations With Fractions

Solve for x: $\frac{3}{2}x+\frac{1}{8}=10$

Possible Answers:

$5 \frac{5}{6}$

$9 \frac{7}{12}$

$6 \frac{7}{12}$

$6\frac{5}{8}$

$5 \frac{1}{4}$

Correct answer:

$6 \frac{7}{12}$

Explanation:

To solve, use inverse opperations: do the opposite steps in the opposite order. Order of opperations is usually PEMDAS, with addition and subtraction last, so we'll do addition/subtraction first:

$\frac{3}{2}x+\frac{1}{8}=10$ since it says to add $\frac{1}{8}$ , we will do the opposite and subtract $\frac{1}{8}$ from both sides:

$\frac{3}{2}x=9 \frac{7}{8}$ Next we will address multiplication/division. Right now we are multiplying times the fraction $\frac{3}{2}$ . Now we want to multiply both sides times its opposite, the reciprocal $\frac{2}{3}$ :

$x= \frac{2}{3}*(9 \frac{7}{8})$ The easiest way to do this is to think of the mixed number $9 \frac{7}{8}$ as the addition $9+ \frac{7}{8}$ and multiply each part times $\frac{2}{3}$ :

$\frac{9}{1}* \frac{2}{3}= 6; \frac{7}{8}* \frac{2}{3} = \frac{7}{12}$

So our answer is $x=6 \frac{7}{12}$

Report an Error

Example Question #12 : Two Step Equations With Fractions

Solve for

$\frac{1}{8}\ X - 10 = 6$

Possible Answers:

128

116

Correct answer:

128

Explanation:

$\frac{1}{8} X - 10 = 6$

Add to each side

$\frac{1}{8}\ X = 16$

Divide both sides by $\frac{1}{8}$ , or multiply by the reciprocal which is $\frac{8}{1}$

X = 128

Report an Error

Example Question #13 : Two Step Equations With Fractions

Solve the following equation for x.

$\frac{3}{4}x+\frac{2}{3}=\frac{1}{6}x-\frac{5}{12}$

Possible Answers:

$-\frac{7}{2}$

$-\frac{13}{7}$

$\frac{91}{144}$

$\frac{7}{15}$

Correct answer:

$-\frac{13}{7}$

Explanation:

To solve equations with fractions, follow the same method as with integers. Collect all the terms with the variable on one side and the terms without variables on the other.

$\frac{3}{4}x-\frac{1}{6}x=-\frac{5}{12}-\frac{2}{3}$

In order to combine the like terms (variables vs. non-variables), the denominators of the fractions must be the same.

$\frac{9}{12}x-\frac{2}{12}x=-\frac{5}{12}-\frac{2}{3}$

$\frac{7}{12}x=-\frac{13}{12}$

$x=-\frac{13}{7}$

Report an Error

Example Question #71 : Two Step Equations

Solve this equation: $6x-\frac{5}{2}=\frac{7}{2}$

Possible Answers:

x=3

The answer is not here.

No solution

x=2

x=-1

Correct answer:

The answer is not here.

Explanation:

$6x-\frac{5}{2}=\frac{7}{2}$

Move all fractions to one side:

$6x=\frac{7}{2}+\frac{5}{2}$

Simplify:

6x=6

x=1

Report an Error

Example Question #12 : Two Step Equations With Fractions

Solve the two-step equation. Find the value of .

$\frac{x}{4} + 222 = 628$

Possible Answers:

x = 2278

x = 212.5

x = 2726

x = 101.5

x = 1624

Correct answer:

x = 1624

Explanation:

x / 4 + 222 = 628

- 222 - 222

x / 4 = 406

*4 *4

x = 1624

Check your answer by substituting 1624 back in for x and solving the problem. This time both sides of the equation should match.

Report an Error

Example Question #16 : Two Step Equations With Fractions

Solve for :

$\frac{1}{8}x - 14 = 12$

Possible Answers:

208

118

3.25

Correct answer:

208

Explanation:

To solve for the variable, we will need to isolate the variable on one side of the equation and all other contstants on the other side. To do this, apply the opposite operation to manipulate the equation.

First, add to both sides:

$\frac{1}{8}x - 14 = 12$

$\frac{1}{8}x = 26$

Next, multiply both sides by to solve for :

x = 208

Report an Error

Example Question #17 : Two Step Equations With Fractions

Solve for :

$\frac{23}{3y} = 3$

Possible Answers:

$\frac{9}{23}$

$\frac{23}{9}$

Correct answer:

$\frac{23}{9}$

Explanation:

First, multiply both sides by :

$\frac{23}{3y} = 3$

23 = 9y

Next, divide both sides by to solve for :

$y = \frac{23}{9}$

Report an Error

Example Question #18 : Two Step Equations With Fractions

Solve for :

$\frac{2}{3}x-\frac{4}{3}=\frac{5}{3}$

Possible Answers:

None of the other answers.

$x=\frac{23}{6}$

$x=\frac{9}{2}$

$x=\frac{6}{23}$

$x=\frac{2}{9}$

Correct answer:

$x=\frac{9}{2}$

Explanation:

$\frac{2}{3}x-\frac{4}{3}=\frac{5}{3}$

Start by isolating the fraction attached the x variable:

$\frac{2}{3}x{\color{Red} -\frac{4}{3}+\frac{4}{3}}=\frac{5}{3}+\frac{4}{3}$

The red terms cancel out.

We add the right side as usual.

$\frac{2}{3}x=\frac{9}{3}$

Reduce fractions where able and multiply by the reciprocal to isolate x:

${\color{Red} \frac{3}{2}*\frac{2}{3}}x=\frac{9}{3}*\frac{3}{2}$

The red terms cancel to 1 and the right is multiplied as usual.

$x=\frac{9}{2}$

Report an Error

View Pre-Algebra Tutors

Masoud
Certified Tutor

University of Guilan,, Bachelor of Science, Biological/Biosystems Engineering. University of Tehran, Master of Science, Anima...

View Pre-Algebra Tutors

Sumit
Certified Tutor

Calcutta University, Bachelor of Science, Mathematics. Indian Statistical Institute, Master of Science, Mathematics.

View Pre-Algebra Tutors

Arnav
Certified Tutor

Rutgers University-Newark, Bachelor of Science, Biomedical Engineering.

All Pre-Algebra Resources

11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Math Tutors in Seattle, Algebra Tutors in San Diego, Physics Tutors in Chicago, Spanish Tutors in Houston, Algebra Tutors in Houston, English Tutors in Philadelphia, ISEE Tutors in Los Angeles, Spanish Tutors in Washington DC, GRE Tutors in Philadelphia, French Tutors in Houston

Popular Courses & Classes

MCAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Miami, SSAT Courses & Classes in New York City, ISEE Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Phoenix, ACT Courses & Classes in San Diego, SAT Courses & Classes in Chicago, ISEE Courses & Classes in Los Angeles, Spanish Courses & Classes in Seattle, ACT Courses & Classes in Atlanta

Popular Test Prep

SSAT Test Prep in Chicago, ACT Test Prep in Atlanta, ISEE Test Prep in New York City, SSAT Test Prep in New York City, MCAT Test Prep in Phoenix, MCAT Test Prep in Houston, ISEE Test Prep in Dallas Fort Worth, ACT Test Prep in Philadelphia, LSAT Test Prep in Phoenix, LSAT Test Prep in Dallas Fort Worth

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

Pre-Algebra : Algebraic Equations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #4 : Two Step Equations With Fractions

Example Question #5 : Two Step Equations With Fractions

Example Question #11 : Two Step Equations With Fractions

Example Question #12 : Two Step Equations With Fractions

Example Question #13 : Two Step Equations With Fractions

Example Question #71 : Two Step Equations

Example Question #12 : Two Step Equations With Fractions

Example Question #16 : Two Step Equations With Fractions

Example Question #17 : Two Step Equations With Fractions

Example Question #18 : Two Step Equations With Fractions

All Pre-Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: