We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : How to solve two-step 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 #563 : Algebra 1

Solve for :

4 (x +6) + 11 = 6 (x + 7) - x

Possible Answers:

x = -7

$x = 3 \frac{1}{2}$

The equation has no solution.

$x = -3 \frac{1}{2}$

x =7

Correct answer:

x = -7

Explanation:

4 (x +6) + 11 = 6 (x + 7) - x

$4 \cdot x +4 \cdot 6 + 11 = 6 \cdot x + 6 \cdot 7 - x$

4 x +24 + 11 = 6x + 42 - x

4 x +35 = 5x + 42

4 x +35 -4x -42 = 5x + 42-4x -42

-7 = x

Report an Error

Example Question #31 : How To Solve Two Step Equations

Solve for .

x^2-7x+3=x^2-6x-2

Possible Answers:

x=-5

x=5

x=-1

x=1

x=10

Correct answer:

x=5

Explanation:

x^2-7x+3=x^2-6x-2

Notice that x^2 can be canceled out by subtracting it from both sides.

x^2-x^2-7x+3=x^2-x^2-6x-2

-7x+3=-6x-2

Now, we can isolate . First, we need to get all the variables on the same side by adding to each side.

-7x+6x+3=-6x+6x-2

-x+3=-2

Subtract from both sides.

-x+3-3=-2-3

-x=-5

Finally, multiply both sides by .

-1(-x)=-1(-5)

x=5

Report an Error

Example Question #32 : How To Solve Two Step Equations

Solve for :

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

Possible Answers:

$x = -\frac{9}{10}$

The equation has no solution.

x = 0

x = 9

x = -9

Correct answer:

The equation has no solution.

Explanation:

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

$5 \cdot x - 5 \cdot 4 + 5 \cdot x - 5 \cdot 5 = 2 \cdot x - 2 \cdot 4 + 4 \cdot 2x - 4 \cdot 7$

5x - 20 + 5 x - 25 = 2 x - 8 + 8x - 28

10x - 45 = 10x - 36

10x - 45 - 10x = 10x - 36- 10x

- 45 = - 36

This statement is identically false, so the original equation has no solution.

Report an Error

Example Question #565 : Linear Equations

Solve for :

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

Possible Answers:

$x = \frac{7}{4}$

$x = \frac{4}{7}$

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

x = 2

x = 3

Correct answer:

x = 2

Explanation:

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

$12 \cdot \frac{3}{4} x =12 \cdot \left ( \frac{5}{12} x + \frac{2}{3} \right )$

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

$\frac{3}{1} \cdot \frac{3}{1} x =\frac{1}{1}\cdot \frac{5}{1} x +\frac{4}{1}\cdot \frac{2}{1}$

9x =5x +8

9x-5x =5x -5x +8

4x =8

$4x \div 4=8\div 4$

x = 2

Report an Error

Example Question #566 : Linear Equations

Solve for :

$\frac{3}{5} x + \frac{3}{20} = \frac{4}{5}$

Possible Answers:

$x = \frac{39}{100}$

$x = \frac{4}{25}$

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

$x = \frac{19}{12}$

$x = \frac{21}{100}$

Correct answer:

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

Explanation:

$\frac{3}{5} x + \frac{3}{20} = \frac{4}{5}$

$20 \cdot \left (\frac{3}{5} x + \frac{3}{20} \right ) =20 \cdot \frac{4}{5}$

$\frac{20}{1} \cdot \frac{3}{5} x + \frac{20}{1} \cdot \frac{3}{20} =\frac{20}{1} \cdot \frac{4}{5}$

$\frac{4}{1} \cdot \frac{3}{1} x + \frac{1}{1} \cdot \frac{3}{1} =\frac{4}{1} \cdot \frac{4}{1}$

12x+3=16

12x+3-3=16-3

12x=13

$12x\div 12=13\div 12$

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

Report an Error

Example Question #32 : How To Solve Two Step Equations

Solve for :

$\frac{1}{2} x - 4 = \frac{3}{10}x + \frac{2}{5}$

Possible Answers:

$x=\frac{22}{5}$

x=22

x=11

$x=\frac{11}{5}$

$x=\frac{44}{5}$

Correct answer:

x=22

Explanation:

$\frac{1}{2} x - 4 = \frac{3}{10}x + \frac{2}{5}$

$10 \cdot \left (\frac{1}{2} x - 4 \right )=10 \cdot \left ( \frac{3}{10}x + \frac{2}{ 5} \right )$

$\frac{10}{1} \cdot \frac{1}{2} x - \frac{10}{1} \cdot \frac{4}{1} \right )=\frac{10}{1} \cdot \frac{3}{10}x +\frac{10}{1} \cdot \frac{2}{ 5}$

$\frac{5}{1} \cdot \frac{1}{1} x - \frac{10}{1} \cdot \frac{4}{1} \right )=\frac{1}{1} \cdot \frac{3}{1}x +\frac{2}{1} \cdot \frac{2}{ 1}$

5x-40 = 3x+4

5x-40 -3x +40= 3x +4 -3x +40

2x=44

x=22

Report an Error

Example Question #567 : Linear Equations

Solve for :

5 (x - 4) + 2 (x - 3) = 3 (x - 4) + 2 (2x - 7)

Possible Answers:

The solution set is the set of all real numbers.

x = 0

$x = \frac{26}{7}$

x = -26

x = 1

Correct answer:

The solution set is the set of all real numbers.

Explanation:

5 (x - 4) + 2 (x - 3) = 3 (x - 4) + 2 (2x - 7)

$5 \cdot x -5 \cdot 4 + 2 \cdot x - 2 \cdot 3 = 3 \cdot x - 3 \cdot 4 + 2 \cdot 2x - 2 \cdot 7$

5x - 20 + 2 x - 6 = 3x - 12 + 4x - 14

7x - 26 = 7x - 26

This statement is identically true; therefore, the solution set is the set of all real numbers.

Report an Error

Example Question #33 : How To Solve Two Step Equations

Call the three angles of a triangle $\angle1,\angle2,\angle3$ . The measure of $\angle2$ is twenty degrees more than that of $\angle 1$ ; the measure of $\angle3$ is forty degrees less than twice that of $\angle 1$ . What is the greatest measure of any of the three angles of the triangle?

Possible Answers:

$50^{\circ }$

$70^{\circ }$

$60^{\circ }$

$120^{\circ }$

$100^{\circ }$

Correct answer:

$70^{\circ }$

Explanation:

Call the measure of $\angle1$ . Since the measure of $\angle2$ is twenty degrees more than that of $\angle 1$ , we can say that $\angle2$ has measure x + 2 0 . Since the measure of $\angle3$ is forty degrees less than twice that of $\angle 1$ , we can say that $\angle3$ has measure 2x-40 .

The sum of the measures of the three angles of a triangle is 180, so we can set up and solve an equation that sets the sum of these three expressions equal to 180:

x + (x + 20) + (2x - 40) = 180

x + x+ 2x + 20 - 40= 180

4x - 20 = 180

4x = 200

x = 50

Substitute 50 for in the other two expressions:

x + 20 = 50 + 20 = 70

$2x-40 = 2\cdot50 - 40 = 60$

The triangle has angles measuring $50^{\circ }, 60^{\circ },70^{\circ }$ , so the answer to the question is $70^{\circ }$ .

Report an Error

Example Question #34 : How To Solve Two Step Equations

Solve for :

5h + 7k = 12

Possible Answers:

$h =\frac{ 7k-12}{5}$

$h =\frac{ 7k}{5}-12$

$h =-\frac{ 7k}{5}+12$

$h =\frac{ - 7k+8 4}{5}$

$h =\frac{ - 7k+12}{5}$

Correct answer:

$h =\frac{ - 7k+12}{5}$

Explanation:

5h + 7k = 12

5h + 7k - 7k = 12- 7k

5h = 12- 7k

$\frac{5h}{5} =\frac{ 12- 7k}{5}$

$h =\frac{ - 7k+12}{5}$

Report an Error

Example Question #572 : Linear Equations

Find the value of in the following linear equation and select the correct answer from the choices listed below.

2x+8=13

Possible Answers:

$-\frac{5}{2}$

$\frac{5}{2},-\frac{5}{2}$

$\frac{5}{2}$

Correct answer:

$\frac{5}{2}$

Explanation:

2x+8=13

Solve equation by using inverse order of operations to get by itself.

Order of operations: PEMDAS. Addition and subtraction usually come last, so when using inverse order of operations to "undo an expression," they come first. 8 is being added to , so subtract 8 from both sides in order to get alone.

2x+8=13

2x=5

Next comes multiplication/division. is being multiplied by 2, so divide both sides by 2 to get on its own.

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

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

Report an Error

View Algebra Tutors

Dossevi
Certified Tutor

cole Ste Genevive Versailles, Bachelor of Science, Mathematics. Institut National Polytechnique de Grenoble, Master of Scienc...

View Algebra Tutors

Keith
Certified Tutor

Xavier University, Bachelor in Business Administration, Accounting. Ohio University-Main Campus, Masters in Education, Mathem...

View Algebra Tutors

Blossom
Certified Tutor

University of Maryland-Baltimore County, Bachelor of Science, Computer Science.

All Algebra 1 Resources

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

Popular Subjects

Spanish Tutors in Phoenix, Statistics Tutors in San Diego, MCAT Tutors in Dallas Fort Worth, Physics Tutors in Houston, French Tutors in Denver, Chemistry Tutors in Phoenix, Math Tutors in Miami, French Tutors in Los Angeles, GRE Tutors in New York City, Calculus Tutors in Philadelphia

Popular Courses & Classes

SSAT Courses & Classes in Miami, SAT Courses & Classes in Chicago, SSAT Courses & Classes in Houston, GRE Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Boston, MCAT Courses & Classes in Seattle, Spanish Courses & Classes in Chicago, ACT Courses & Classes in Seattle, ISEE Courses & Classes in Phoenix, Spanish Courses & Classes in Phoenix

Popular Test Prep

SAT Test Prep in Houston, SSAT Test Prep in New York City, ACT Test Prep in Seattle, SAT Test Prep in Dallas Fort Worth, LSAT Test Prep in San Diego, GMAT Test Prep in Boston, SSAT Test Prep in Los Angeles, SSAT Test Prep in Phoenix, LSAT Test Prep in Los Angeles, MCAT Test Prep in Boston

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 : How to solve two-step equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #563 : Algebra 1

Example Question #31 : How To Solve Two Step Equations

Example Question #32 : How To Solve Two Step Equations

Example Question #565 : Linear Equations

Example Question #566 : Linear Equations

Example Question #32 : How To Solve Two Step Equations

Example Question #567 : Linear Equations

Example Question #33 : How To Solve Two Step Equations

Example Question #34 : How To Solve Two Step Equations

Example Question #572 : Linear Equations

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: