Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Equations / Solution Sets

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

← Previous 1 2 3 4 5 6 7 8 9 10 Next →

Example Question #1 : How To Find A Solution Set

Solve for :

-3x + 12 = -3

Possible Answers:

Correct answer:

Explanation:

Subtract 12 from both sides:

–3x = –15

Divide both sides by –3:

x = 5

Report an Error

Example Question #21 : Equations / Solution Sets

Solve for :

x(x - 2) = x^2 -8

Possible Answers:

Correct answer:

Explanation:

Distribute the x through the parentheses:

x² –2x = x² – 8

Subtract x² from both sides:

–2x = –8

Divide both sides by –2:

x = 4

Report an Error

Example Question #6 : How To Find A Solution Set

Solve for :

$\dpi{130} \sqrt[3]{100-x} - 5 = 0$

Possible Answers:

$x = -25 \textrm{ or } x = 225$

x = 225

The equation has no solution.

x = 125

x = -25

Correct answer:

x = -25

Explanation:

Add 5 to both sides to isolate the cube root:

$\dpi{130} \sqrt[3]{100-x} - 5+ 5 = 0+ 5$

$\dpi{130} \sqrt[3]{100-x} = 5$

Cube both sides:

$\dpi{130} \left (\sqrt[3]{100-x} \right) ^{3}= 5 ^{3}$

100-x = 125

To isolate , move it to the right side of the equation. We choose the right side instead of the left side so as to make positive:

100-x +x= 125+x

100 = 125+x

Subtract 125 from both sides to isolate :

100 - 125 = 125 - 125 +x

-25 = x

Report an Error

Example Question #1 : Setting Up Expressions

We have three cats, Chai, Sora, and Newton. Chai is 3 years old. Sora two years older than twice Chai's age. Newton is one year younger than one-fourth of Sora's age. How old are Sora and Newton?

Possible Answers:

Sora: 3 years

Newton: not born yet

Sora: 1 year

Newton: 8 years

Sora: 5 years

Newton: 6 years

Sora: 8 years

Newton: 1 year

Sora: 4 years

Newton: one half year

Correct answer:

Sora: 8 years

Newton: 1 year

Explanation:

To make this much easier, translate the word problem into a system of three equations.

C=3

S=2C+2

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

We have C for Chai, S for Sora, and N for Newton. To find Sora's age, plug in into .

S=2(3)+2=8

Sora is 8 years old. Use this to find Newton's age.

$N=\frac{1}{4}(8)-1=1$

Newton is one year old. So the answer is:

Sora, 8 years

Newton, 1 year

Report an Error

Example Question #1 : Solving Equations And Inequallities

Give all real solutions of the following equation:

$x^{4} - 13x^{2} + 36 = 0$

Possible Answers:

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

The equation has no real solutions.

$\left \{ 4,9\right \}$

$\left \{ -9,-4,4,9\right \}$

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

Correct answer:

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

Explanation:

By substituting $u = x^{2}$ - and, subsequently, $u^{2} =\left ( x^{2} \right )^{2} = x^{4}$ this can be rewritten as a quadratic equation, and solved as such:

$x^{4} - 13x^{2} + 36 = 0$

$u^{2} - 13u + 36 = 0$

We are looking to factor the quadratic expression as (u+?)(u+?) , replacing the two question marks with integers with product 36 and sum ; these integers are -9,-4 .

(u-9)(u-4) = 0

Substitute back:

$(x^{2}-9)(x^{2}-4) = 0$

These factors can themselves be factored as the difference of squares:

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

Set each factor to zero and solve:

$x-3 = 0 \Rightarrow x = 3$

$x-2= 0 \Rightarrow x = 2$

$x+2 = 0 \Rightarrow x = - 2$

$x+3 = 0 \Rightarrow x = - 3$

The solution set is $\left \{ -3, -2, 2, 3\right \}$ .

Report an Error

Example Question #22 : Equations / Solution Sets

Solve for :

$\frac{6}{x-2} + 1 = x$

Possible Answers:

$x = 2 \textrm{ or } x = 4$

There is no solution.

x = -1

$x = -1 \textrm{ or } x = 4$

$x = 1 \textrm{ or } x = -4$

Correct answer:

$x = -1 \textrm{ or } x = 4$

Explanation:

Subtract 1 from both sides, then multiply all sides by x-2 :

$\frac{6}{x-2} + 1 = x$

$\frac{6}{x-2} + 1 - 1 = x- 1$

$\frac{6}{x-2} = x- 1$

$\frac{6}{x-2} \cdot (x-2) = \left (x- 1 \right ) \cdot (x-2)$

$6 = x^{2} -3x + 2$

$6 - 6 = x^{2} -3x + 2 - 6$

$0 = x^{2} -3x -4$

A quadratic equation is yielded. We can factor the expression, then set each individual factor to 0.

$x^{2} -3x -4 =0$

(x-4) (x+1) = 0

$x-4 = 0 \Rightarrow x = 4$

$x+1 = 0 \Rightarrow x = -1$

Both of these solutions can be confirmed by substitution.

Report an Error

Example Question #23 : Equations / Solution Sets

Solve for :

$x = \sqrt{2x-1} +8$

Possible Answers:

x = 5

$x = -13 \textrm{ or } x = 13$

$x = 5 \textrm{ or } x = 13$

$x = -5 \textrm{ or } x = 5$

x = 13

Correct answer:

x = 13

Explanation:

Isolate the radical, square both sides, and solve the resulting quadratic equation.

$x = \sqrt{2x-1} +8$

$x - 8 = \sqrt{2x-1} +8 -8$

$x - 8 = \sqrt{2x-1}$

$\left (x -8 \right )^{2} =\left ( \sqrt{2x-1} \right )^{2}$

$x^{2} - 2 \cdot x \cdot 8 + 8^{2} = 2x - 1$

$x^{2} - 16 x + 64 = 2x - 1$

$x^{2} - 16 x + 64 - 2x + 1 = 2x - 1 - 2x + 1$

$x^{2} - 18 x + 65 = 0$

Factor the expression at left by finding two integers whose product is 65 and whose sum is ; they are -13,-5 .

(x-13) (x-5 ) = 0

Set each linear binomial to 0 and solve for to find the possible solutions.

x-13 = 0

x = 13

x-5 = 0

x = 5

Substitute each for .

x=5:

$x = \sqrt{2x-1} +8$

$5 = \sqrt{2 \cdot 5-1} +8$

$5 = \sqrt{9} +8$

5 = 3 +8

5 = 11

This is a false statement, so 5 is a false "solution".

x=13:

$x = \sqrt{2x-1} +8$

$13 = \sqrt{2 \cdot 13-1} +8$

$13= \sqrt{25} +8$

13 = 5 +8

13 = 13

This is a true statement, so 13 is the only solution of the equation.

Report an Error

Example Question #21 : Equations / Solution Sets

Solve the equation for .

$\left | 5x-4\right |=\left | 2x+7\right |$

Possible Answers:

$x=0\;or\;x=-2$

$x=\frac{11}{3}\;or\;x=-\frac{3}{7}$

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

$x=\frac{11}{7}\;or\;x=-\frac{11}{7}$

$x=\frac{3}{7}\:\: or\: \:x=-\frac{11}{3}$

Correct answer:

$x=\frac{11}{3}\;or\;x=-\frac{3}{7}$

Explanation:

The two sides of the equation will be equal if the quantities inside the absolute value signs are equal or equal with opposite signs.

From this, you get two equations.

5x-4=2x+7 or 5x-4=-(2x+7)

3x=11 7x=-3

$x=\frac{11}{3}$ $x=-\frac{3}{7}$

Report an Error

Example Question #25 : Equations / Solution Sets

Find the solution, in the form (x,y) , to the following system of equations:

4x+3y=9

-3x-5y=-26

Possible Answers:

(1,-3)

(3,-7)

(-3,7)

(3,-1)

(-1,4)

Correct answer:

(-3,7)

Explanation:

(1) $ $ $ $ 4x+3y=9

(2)$ $ $ $ -3x-5y=-26

Multiply (1) by 3, multiply (2) by 4:

$3\cdot (4x+3y=9)=12x+9y=27$

$4\cdot(-3x-5y=-26)=-12x-20y=-104$

Add the two resulting solutions:

(12x+9y)+(-12x-20y)=27-104

-11y=-77

y=7

Substitute y=7 into (1) and solve for :

4x+3(7)=9

4x+21-21=9-21

4x=-12

x=-3

Report an Error

Example Question #26 : Equations / Solution Sets

2x-7=11

Possible Answers:

x=5

No solution.

None of the other answers.

x=9

x=2

Correct answer:

x=9

Explanation:

To find the solution isolate the variable on one side of the equation.

2x-7=11

2x=18

x=9

To check to see if this is the correct solution, plug the value of x back into the equation and solve:

2(9)-7=11

18-7=11

11=11

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 10 Next →

View Algebra Tutors

Ping
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Computer Science. University of North Texas, Master of Arts, Education.

View Algebra Tutors

Shrikar
Certified Tutor

University of South Florida-Main Campus, Bachelor of Science, Biomedical Sciences.

View Algebra Tutors

Eliza
Certified Tutor

University of Pennsylvania, Bachelor in Arts, Economics.

All Algebra 1 Resources

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

Popular Subjects

SAT Tutors in Dallas Fort Worth, Calculus Tutors in Phoenix, English Tutors in Atlanta, Statistics Tutors in Denver, SAT Tutors in Miami, MCAT Tutors in Phoenix, SAT Tutors in Washington DC, Statistics Tutors in Atlanta, Spanish Tutors in Houston, Computer Science Tutors in Denver

Popular Courses & Classes

SAT Courses & Classes in Phoenix, Spanish Courses & Classes in Atlanta, Spanish Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Phoenix, SAT Courses & Classes in Houston, SSAT Courses & Classes in Boston, GMAT Courses & Classes in Seattle, ISEE Courses & Classes in Atlanta, ISEE Courses & Classes in Philadelphia, SAT Courses & Classes in San Diego

Popular Test Prep

SSAT Test Prep in Boston, GRE Test Prep in Boston, ISEE Test Prep in San Francisco-Bay Area, GRE Test Prep in San Diego, SAT Test Prep in San Francisco-Bay Area, GRE Test Prep in Philadelphia, SAT Test Prep in Atlanta, GMAT Test Prep in Houston, SSAT Test Prep in Atlanta, LSAT 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

Algebra 1 : Equations / Solution Sets

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Find A Solution Set

Example Question #21 : Equations / Solution Sets

Example Question #6 : How To Find A Solution Set

Example Question #1 : Setting Up Expressions

Example Question #1 : Solving Equations And Inequallities

Example Question #22 : Equations / Solution Sets

Example Question #23 : Equations / Solution Sets

Example Question #21 : Equations / Solution Sets

Example Question #25 : Equations / Solution Sets

Example Question #26 : Equations / Solution Sets

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: