GMAT Math : Linear Equations, One Unknown

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1361 : Gmat Quantitative Reasoning

For what value of $\small N$ would the following equation have no solution?

$\small \small 3 (4x - 7) + 12 = 2 (5x - 3) + N (x - 3)$

Possible Answers:

$\small N= 2$

$\small \small N= 1$

$\small \small N= -1$

$\small N= -2$

The equation must always have at least one solution regardless of the value of $\small N$ .

Correct answer:

$\small N= 2$

Explanation:

Simplify both sides of the equation as much as possible, and solve for $\small x$ in the equation in terms of $\small N$ :

$\small \small \small 3 (4x - 7) + 12 = 2 (5x - 3) + N (x - 3)$

$\small 3 \cdot 4x - 3 \cdot 7 + 12 = 2 \cdot 5x - 2 \cdot 3 + N \cdot x - N \cdot 3$

$\small 12x - 21 + 12 = 10x - 6 + Nx - 3N$

$\small 12x - 9 = (10+N)x + (- 6 - 3N)$

$\small \small 12x - (10+N)x = (- 6 - 3N) + 9$

$\small (2-N)x = 3 - 3N$

$\small x = \frac{3 - 3N}{2 -N}$

$\small x$ has exactly one solution unless the denominator is 0 - that is, $\small N = 2$ . We make sure that this value renders no solution by substituting:

$\small \small \small 3 (4x - 7) + 12 = 2 (5x - 3) + N (x - 3)$

$\small \small \small \small 3 (4x - 7) + 12 = 2 (5x - 3) + 2 (x - 3)$

$\small 12x - 21 + 12 = 10x - 6 + 2x - 6$

$\small 12x - 9 = 12x - 12$

$\small - 9 = - 12$

The equation has no solution, and $\small N = 2$ is the correct answer.

Report an Error

Example Question #1 : Solving Linear Equations With One Unknown

Solve for :

n+2=-14-n

Possible Answers:

Correct answer:

Explanation:

n+2=-14-n

n+n=-14-2

2n=-16

n=-8

Report an Error

Example Question #1362 : Gmat Quantitative Reasoning

Solve for :

-6x-20=-2x+4(1-3x)

Possible Answers:

Correct answer:

Explanation:

-6x-20=-2x+4(1-3x)

-6x-20=-2x+4-12x

-6x-20=-14x+4

-6x+14x=4+20

8x=24

x=3

Report an Error

Example Question #1363 : Gmat Quantitative Reasoning

Solve for :

-14+6b+7-2b=1+5b

Possible Answers:

Correct answer:

Explanation:

-14+6b+7-2b=1+5b

-7+4b=1+5b

4b-5b=1+7

-b=8

b=-8

Report an Error

Example Question #1 : Linear Equations, One Unknown

What is the midpoint coordinate of (1,4) and (7,10) ?

Possible Answers:

(3,3)

(6,6)

(7,4)

(4,7)

Correct answer:

(4,7)

Explanation:

Midpoint formula:

$\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$

$(1,4)\ and\ (7,10)$

$\left(\frac{1+7}{2},\frac{4+10}{2}\right)$

$\left(\frac{8}{2},\frac{14}{2}\right)$

Report an Error

Example Question #4 : Solving Linear Equations With One Unknown

What is the midpoint coordinate of (1,2) and (5,2) ?

Possible Answers:

(2,0)

(2,3)

(6,4)

(3,2)

Correct answer:

(3,2)

Explanation:

Midpoint formula:

$\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$

$(1,2)\ and\ (5,2)$

$\left(\frac{1+5}{2},\frac{2+2}{2}\right)$

$\left(\frac{6}{2},\frac{4}{2}\right)$

Report an Error

Example Question #286 : Algebra

What is the midpoint coordinate of (-2,-1) and (-8,7) ?

Possible Answers:

(5,3)

(3,-5)

(3,5)

(-5,3)

Correct answer:

(-5,3)

Explanation:

Midpoint formula:

$\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$

$(-2,-1)\ and\ (-8,7)$

$\left(\frac{-2+-8}{2},\frac{-1+7}{2}\right)$

$\left(\frac{-10}{2},\frac{6}{2}\right)$

Report an Error

Example Question #1 : Linear Equations, One Unknown

Solve the following equation:

$2\left | x-5\right |+16=30$ .

Possible Answers:

x = {-9 : 16}

x = {-2 ; 12}

x = {-7 ; 7}

x = 2

x = {0 ; 10}

Correct answer:

x = {-2 ; 12}

Explanation:

We start by isolating the absolute value expression:

This gives us two cases when we remove the absolute value:

x - 5 = 7 and x - 5 = -7

Then we solve for each case:

$x - 5 = 7 \Rightarrow x = 7 + 5 \Rightarrow x= 12$

$x - 5 = -7 \Rightarrow x = -7 + 5\Rightarrow x= -2$

Report an Error

Example Question #287 : Algebra

Solve for :

5 (N - 6)- 2(N + 4) = 7 (N + 5)

Possible Answers:

$N = -18 \frac{1}{4}$

$N = -\frac{3}{4}$

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

$N = -25 \frac{3}{4}$

The equation has no solution.

Correct answer:

$N = -18 \frac{1}{4}$

Explanation:

5 (N - 6)- 2(N + 4) = 7 (N + 5)

$\left (5 N - 30 \right ) - \left (2 N + 8 \right )= 7N + 35$

5 N - 30 - 2 N - 8= 7N + 35

3 N - 3 8= 7N + 35

3 N - 3 8+ 38 = 7N + 35 + 38

3 N = 7N + 73

3 N-7N = 7N + 73 -7N

-4N = 73

$N = \frac{73}{-4}= - 18 \frac{1}{4}$

Report an Error

Example Question #288 : Algebra

Solve for :

$\left (4x + 7 \right ) + 2 (x + 15 ) = 3(x-17)$

Possible Answers:

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

$x = -9\frac{7}{9}$

$x = -29 \frac{1}{3}$

$x = -24\frac{1}{3}$

The equation has no solution.

Correct answer:

$x = -29 \frac{1}{3}$

Explanation:

$\left (4x + 7 \right ) + 2 (x + 15 ) = 3(x-17)$

$\left (4x + 7 \right ) + (2x+30) = 3x-51$

6x+37 = 3x-51

6x+37 - 3x = 3x-51 - 3x

3x+37 = -51

3x = -51 - 37

3x = -88

$x = \frac{-88}{3}= -29 \frac{1}{3}$

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Washington DC, Reading Tutors in Chicago, English Tutors in Denver, Chemistry Tutors in San Diego, SSAT Tutors in Denver, SAT Tutors in Seattle, Biology Tutors in Washington DC, Statistics Tutors in Dallas Fort Worth, ACT Tutors in Boston, English Tutors in Los Angeles

Popular Courses & Classes

Spanish Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in New York City, Spanish Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Chicago, GRE Courses & Classes in Phoenix, SAT Courses & Classes in Philadelphia, GRE Courses & Classes in Atlanta, ISEE Courses & Classes in Boston, SSAT Courses & Classes in Boston, SSAT Courses & Classes in Washington DC

Popular Test Prep

GRE Test Prep in Dallas Fort Worth, LSAT Test Prep in Chicago, MCAT Test Prep in Chicago, MCAT Test Prep in Phoenix, GRE Test Prep in Washington DC, MCAT Test Prep in Atlanta, GRE Test Prep in Denver, SAT Test Prep in Atlanta, ACT Test Prep in Dallas Fort Worth, SSAT 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)

Email address:
Your name:
Feedback:

GMAT Math : Linear Equations, One Unknown

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1361 : Gmat Quantitative Reasoning

Example Question #1 : Solving Linear Equations With One Unknown

Example Question #1362 : Gmat Quantitative Reasoning

Example Question #1363 : Gmat Quantitative Reasoning

Example Question #1 : Linear Equations, One Unknown

Example Question #4 : Solving Linear Equations With One Unknown

Example Question #286 : Algebra

Example Question #1 : Linear Equations, One Unknown

Example Question #287 : Algebra

Example Question #288 : Algebra

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details