We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Linear / Rational / Variable 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 #3 : Solving Equations

Solve for :.

18x^3 - 8x = 0

Possible Answers:

$\left \{ - \frac{3}{2}, \frac{3}{2} \right\}$

$\left \{-\frac{2}{3}, \frac{2}{3} \right \}$

$\left \{-\frac{2}{3}, 0, \frac{2}{3} \right \}$

$\left \{ \frac{3}{2}, 0, -\frac{3}{2} \right\}$

Correct answer:

$\left \{-\frac{2}{3}, 0, \frac{2}{3} \right \}$

Explanation:

First factor the expression by pulling out :

18x^3 - 8x = 0

2x(9x^2-4) = 0

Factor the expression in parentheses by recognizing that it is a difference of squares:

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

Set each term equal to 0 and solve for the x values:

$2x=0 \rightarrow x=0$

$3x+2=0\rightarrow x=-\frac{2}{3}$

$3x-2=0\rightarrow x=\frac{2}{3}$

Report an Error

Example Question #21 : How To Find The Solution To An Equation

Possible Answers:

$\frac{2}{3}$

$\frac{4}{3}$

$\frac{7}{9}$

$\frac{5}{3}$

$\frac{5}{9}$

Correct answer:

$\frac{5}{9}$

Explanation:

1. First, simplify the numerator by finding a common denominator:

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

2. Next, simplify the denominator. These fractions can be added together without any additional work:

$\frac{9}{5}+\frac{6}{5}= \frac{15}{5}=3$

3. Then, simplify by multiplying top and bottom by the recriprocal of the denominator:

$\frac{\frac{5}{3}}{3}\cdot\frac{\frac{1}{3}}{\frac{1}{3}}=\frac{\frac{5}{9}}{1}=\frac{5}{9}$

Report an Error

Example Question #22 : How To Find The Solution To An Equation

$A\bigtriangledown B = \frac{-A^2+3(-B)^2}{\frac{2}{A}+\frac{1}B{}}$

$4\bigtriangledown 2=$

Possible Answers:

$-\frac{3}{2}$

$-\frac{1}{2}$

Correct answer:

Explanation:

Here, A=4,B=2 . Plug these values in and simplify.

Start with the numerator first:

-A^2 +3(-B)^2 = -(4)^2 +3(-2)^2= -16 +12=-4

Then do the same in the denominator:

$\frac{2}{A}+\frac{1}{B}= \frac{2}{4}+\frac{1}{2}= \frac{1}{2}+\frac{1}{2}=1$

Finally, combine the two results to find the solution:

$\frac{-4}{1}=-4$

Report an Error

Example Question #151 : Understanding Quadratic Equations

Solve for :

$(x-3)^{2}=36$

Possible Answers:

(9,3)

(9,-3)

None of the other answers

(6,-6)

(3,-9)

Correct answer:

(9,-3)

Explanation:

To solve this equation, you must first eliminate the exponent from the (x-3) by taking the square root of both sides:

$\sqrt{(x-3)^{2}}=\sqrt{36}$

Since the square root of 36 could be either or , there must be 2 values of . So, solve for

x-3=-6

and

x-3=6

to get solutions of (9,-3) .

Report an Error

Example Question #32 : Solving Equations

Solve for :

ax-b=cd

Possible Answers:

$\frac{cd+a}{b}$

$\frac{a}{cd+b}$

None of the other answers

$\frac{b}{cd+a}$

$\frac{cd+b}{a}$

Correct answer:

$\frac{cd+b}{a}$

Explanation:

To solve for , you must isolate it from the other variables. Start by adding to both sides to give you ax=cd+b . Now, you need only to divide from both sides to completely isolate . This gives you a solution of $x=\frac{cd+b}{a}$ .

Report an Error

Example Question #2 : Solving Equations And Inequallities

Solve for :

6x-3-4x+5=3(x-1)

Possible Answers:

Correct answer:

Explanation:

Combine like terms on the left side of the equation: 2x+2=3(x-1)

Use the distributive property to simplify the right side of the equation: 2x+2=3x-3

Next, move the 's to one side and the integers to the other side: x=5

Report an Error

Example Question #41 : Solving Equations

Solve for :

ex+f=g

Possible Answers:

$\frac{e}{g-f}$

$\frac{e}{g+f}$

$\frac{g+f}{e}$

None of the other answers

$\frac{g-f}{e}$

Correct answer:

$\frac{g-f}{e}$

Explanation:

To solve for , you must isolate it so that all of the other variables are on the other side of the equation. To do this, first subtract from both sides to get ex=g-f . Then, divide both sides by to get $x=\frac{g-f}{e}$ .

Report an Error

Example Question #151 : Equations / Inequalities

The sum of four consecutive integers equal 98. What is the sum of the smallest and the largest number in the set?

Possible Answers:

Correct answer:

Explanation:

Let a variable represent the smallest number in the set. Every consecutive number after the first number will be one unit greater than the other. Then, the four numbers that sum up to 98 are:

(x)+(x+1)+(x+2)+(x+3)=98

where every term in parenthesis represents a number. Add and solve for .

4x+6=98

x=23

The smallest number is , and the largest number is x+3 . Therefore:

x+(x+3)= 23+(23+3)=23+26=49

The correct answer is:

Report an Error

Example Question #152 : Equations / Inequalities

Solve for .

3a+4-4(a+2)=-12a+6(a-2)

Possible Answers:

-8/5

5/8

8/5

-5/8

Correct answer:

-8/5

Explanation:

The question asks for the value of .

To isolate , use the distributive properties to remove the parentheses then combine like terms.

3a+4-4(a+2)=-12a+6(a-2)

3a+4-4a-8=-12a+6a-12

-a-4=-6a-12

Finally isolate by balancing the equation.

5a=-8

a=-8/5

Report an Error

Example Question #153 : Equations / Inequalities

Find the solution to this equation: $10x+25(x-\frac{1}{25})=174$

Possible Answers:

x=5

$x=\frac{1}{5}$

x=-5

None of the other answers.

$x=-\frac{1}{5}$

Correct answer:

x=5

Explanation:

To find the solution to this equation you must completely isolate x.

$10x+25(x-\frac{1}{25})=174$

Start by dealing with the parenthesis first. Distribute the 25:

10x+25x-1=174

Combine the x terms and move the constant over:

35x=175

Finally divide the constant away from x to solve:

x=5

Report an Error

View Algebra Tutors

Dilip
Certified Tutor

University of Calcutta, Bachelor of Science, Physics. Indiana Institute of Technology, Master of Science, Physics.

View Algebra Tutors

Mohammad
Certified Tutor

Rutgers University-New Brunswick, Bachelor of Science, Mathematics. Rutgers University-New Brunswick, Master of Science, Stat...

View Algebra Tutors

Jason
Certified Tutor

Brigham Young University, Bachelor, Neuroscience.

All Algebra 1 Resources

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

Popular Subjects

Reading Tutors in Phoenix, Algebra Tutors in New York City, SAT Tutors in Dallas Fort Worth, Calculus Tutors in Miami, Spanish Tutors in Phoenix, Calculus Tutors in Denver, LSAT Tutors in San Francisco-Bay Area, GRE Tutors in Phoenix, Algebra Tutors in San Diego, MCAT Tutors in Boston

Popular Courses & Classes

GRE Courses & Classes in Seattle, ISEE Courses & Classes in Philadelphia, ISEE Courses & Classes in Atlanta, LSAT Courses & Classes in Seattle, SAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Miami, SAT Courses & Classes in Los Angeles, Spanish Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Chicago, GMAT Courses & Classes in Los Angeles

Popular Test Prep

ACT Test Prep in Miami, MCAT Test Prep in Los Angeles, GRE Test Prep in Los Angeles, GMAT Test Prep in Los Angeles, LSAT Test Prep in Dallas Fort Worth, GRE Test Prep in San Francisco-Bay Area, GMAT Test Prep in Washington DC, LSAT Test Prep in New York City, ACT Test Prep in New York City, GRE 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 1 : Linear / Rational / Variable Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #3 : Solving Equations

Example Question #21 : How To Find The Solution To An Equation

Example Question #22 : How To Find The Solution To An Equation

Example Question #151 : Understanding Quadratic Equations

Example Question #32 : Solving Equations

Example Question #2 : Solving Equations And Inequallities

Example Question #41 : Solving Equations

Example Question #151 : Equations / Inequalities

Example Question #152 : Equations / Inequalities

Example Question #153 : Equations / Inequalities

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: