Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : How to find out when an equation has no solution

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 #1 : How To Find Out When An Equation Has No Solution

Solve the rational equation:

$\small \frac{1}{m+3}+\frac{1}{m-3}=\frac{6}{m^2-9}$

Possible Answers:

$\small m=6$

$\small m=0$

$\small m=3$ or $\small m=-3$

$\small m=\frac{1}{3}$

no solution

Correct answer:

no solution

Explanation:

With rational equations we must first note the domain, which is all real numbers except $\small \small m=-3$ and $\small \small m=3$ . That is, these are the values of $\small m$ that will cause the equation to be undefined. Since the least common denominator of $\small m+3$ , $\small m-3$ , and $\small m^2-9$ is $\small (m+3)(m-3)$ , we can mulitply each term by the LCD to cancel out the denominators and reduce the equation to $\small (m-3)+(m+3)=6$ . Combining like terms, we end up with $\small 2m=6$ . Dividing both sides of the equation by the constant, we obtain an answer of $\small m=3$ . However, this solution is NOT in the domain. Thus, there is NO SOLUTION because $\small m=3$ is an extraneous answer.

Report an Error

Example Question #2 : How To Find Out When An Equation Has No Solution

Find the solution set:

3x+3y=4

x+y=7

Possible Answers:

(4,0)

None of the other answers.

(1,2)

(0,4)

(2,1)

Correct answer:

None of the other answers.

Explanation:

Use the substitution method to solve for the solution set.

1) 3x+3y=4

2) x+y=7

Solve equation 2 for y:

y=-x+7

Substitute into equation 1:

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

3x-3x+21=4

$21\neq4$

If equation 1 was solved for a variable and then substituted into the second equation a similar result would be found. This is because these two equations have No solution. Change both equations into slope-intercept form and graph to visualize. These lines are parallel; they cannot intersect.

*Any method of finding the solution to this system of equations will result in a no solution answer.

Report an Error

Example Question #1 : How To Find Out When An Equation Has No Solution

How many solutions does the equation below have?

9x + 4 = 3(3x + 4)

Possible Answers:

Infinite

No solutions

Two

One

Three

Correct answer:

No solutions

Explanation:

When finding how many solutions an equation has you need to look at the constants and coefficients.

The coefficients are the numbers alongside the variables.

The constants are the numbers alone with no variables.

If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.

9x + 4 = 3(3x + 4)

Use distributive property on the right side first.

9x + 4 = 9x + 12

-9x -9x

$4 \neq 12$

No solutions

Report an Error

Example Question #3 : How To Find Out When An Equation Has No Solution

Solve: $\frac{x^2-1}{x-1} = 2$

Possible Answers:

$\textup{No solution.}$

$\pm1$

Correct answer:

$\textup{No solution.}$

Explanation:

First factorize the numerator.

x^2-1 = (x-1)(x+1)

Rewrite the equation.

$\frac{(x-1)(x+1)}{x-1} = 2$

The x-1 terms can be eliminated.

x+1=2

Subtract one on both sides.

x=1

However, let's substitute this answer back to the original equation to check whether if we will get as an answer.

$\frac{(1)^2-1}{1-1} = 2$

Simplify the left side.

$\frac{0}{0}=2$

The left side does not satisfy the equation because the fraction cannot be divided by zero.

Therefore, x=1 is not valid.

The answer is: $\textup{No solution.}$

Report an Error

Example Question #1 : How To Find Out When An Equation Has No Solution

Solve for :

7x+6-3x=x+8+3x

Possible Answers:

No solution

Correct answer:

No solution

Explanation:

Combine like terms on each side of the equation:

7x+6-3x=x+8+3x

4x+6=4x+8

Next, subtract from both sides.

4x+6-6=4x+8-6

Then subtract from both sides.

4x-4x=4x-4x+2

0=2

This is nonsensical; therefore, there is no solution to the equation.

Report an Error

Example Question #1 : How To Find Out When An Equation Has No Solution

Solve the equation: $\left | 2x+3\right |=-1$

Possible Answers:

$\pm1$

No solution

Correct answer:

No solution

Explanation:

Notice that the end value is a negative. Any negative or positive value that is inside an absolute value sign must result to a positive value.

If we split the equation to its positive and negative solutions, we have:

$A.\: \: 2x+3=-1$

$B. \: \: -(2x+3)=-1$

Solve the first equation.

2x= -1+3

2x=2

x=1

The answer to is: x=1

Solve the second equation.

2x+3=1

2x=-2

x=-1

The answer to is: x=-1

If we substitute these two solutions back to the original equation, the results are positive answers and can never be equal to negative one.

The answer is no solution.

Report an Error

View Algebra Tutors

Midori
Certified Tutor

University of Connecticut, Bachelor in Arts, Applied Mathematics. University of Southern California, Master of Arts Teaching,...

View Algebra Tutors

Mariam
Certified Tutor

Yarmouk University, Bachelor of Science, Mathematics. Touro College, Master of Science, Teacher Education, Multiple Levels.

View Algebra Tutors

Tajrin
Certified Tutor

CUNY Brooklyn College, 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

GMAT Tutors in Denver, Calculus Tutors in Chicago, GRE Tutors in Atlanta, ACT Tutors in Miami, Chemistry Tutors in San Diego, Physics Tutors in Denver, Spanish Tutors in Los Angeles, Reading Tutors in Boston, Algebra Tutors in Chicago, Reading Tutors in Seattle

Popular Courses & Classes

Spanish Courses & Classes in San Diego, ISEE Courses & Classes in New York City, MCAT Courses & Classes in Chicago, SSAT Courses & Classes in Houston, ISEE Courses & Classes in Denver, ACT Courses & Classes in Atlanta, MCAT Courses & Classes in Seattle, MCAT Courses & Classes in Atlanta, SAT Courses & Classes in Denver, SSAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

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

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 find out when an equation has no solution

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Find Out When An Equation Has No Solution

Example Question #2 : How To Find Out When An Equation Has No Solution

Example Question #1 : How To Find Out When An Equation Has No Solution

Example Question #3 : How To Find Out When An Equation Has No Solution

Example Question #1 : How To Find Out When An Equation Has No Solution

Example Question #1 : How To Find Out When An Equation Has No Solution

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: