We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : How to find the solution to an equation

Study concepts, example questions & explanations for ISEE Upper Level Math

Create An Account

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 … 5 6 7 8 9 10 11 12 13 … 18 19 Next →

Example Question #81 : How To Find The Solution To An Equation

x + y = 13

2x - y = 14

What is ?

Possible Answers:

x = 27

x = 4

can be any real number.

x = 9

x = 1

Correct answer:

x = 9

Explanation:

Add the left and right sides of the equations separately:

x + y = 13

$\underline{2x - y = 14}$

$3x\; \; \; \; \; \; = 27$

Divide:

$3x \div 3 = 27\div 3$

x=9

Report an Error

Example Question #82 : How To Find The Solution To An Equation

Give the -intercept of the line through points (4,1) and (6,5) .

Possible Answers:

The line has no -intercept.

$\left ( -7,0 \right )$

$\left ( 3\frac{1}{2 },0 \right )$

$\left ( -3\frac{1}{2 },0 \right )$

$\left ( 7,0 \right )$

Correct answer:

$\left ( 3\frac{1}{2 },0 \right )$

Explanation:

The slope of this line is

$m = \frac{y_{2}-y_{1} }{x_{2}-x_{1}} = \frac{5-1 }{6-4} = \frac{4 }{2} = 2$ .

Let the -intercept be (a,0) . Then, using the slope and point (4,1) , we know that:

$m = \frac{y_{2}-y_{1} }{x_{2}-x_{1}} = \frac{0-1 }{a-4} = 2$

$\frac{-1 }{a-4} = 2$

$\frac{1 }{a-4} = -2$

Take the reciprocal of both sides:

$a-4 =- \frac{1 }{2}$

$a-4+ 4 =- \frac{1 }{2}+ 4$

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

The -intercept is $\left ( 3\frac{1}{2 },0 \right )$ .

Report an Error

Example Question #83 : How To Find The Solution To An Equation

A line through points (6,5 ) and (4,N ) has slope . What is ?

Possible Answers:

N =9

N =1

N =0

N =3

N =5

Correct answer:

N =1

Explanation:

Substitute $x _{1 } = 6, y_{1 }= 5, x _{2 } = 4, y_{2 }= N, m = 2$ into the slope formula:

$\frac{y_{2} -y_{1} }{x_{2} -x_{1}} = m$

$\frac{N -5 }{4 -6} = 2$

$\frac{N -5 }{-2} = 2$

$\frac{N -5 }{-2} \cdot (-2) = 2 \cdot (-2)$

N -5 =-4

N -5 + 5=-4 + 5

N =1

Report an Error

Example Question #84 : How To Find The Solution To An Equation

Give the -intercept of the line through points (4,1) and (6,5) .

Possible Answers:

(0,7)

The line has no -intercept.

$\left ( 0, 3\frac{1}{2 } \right )$

(0,-7)

$\left ( 0,- 3\frac{1}{2 } \right )$

Correct answer:

(0,-7)

Explanation:

The slope of this line is

$m = \frac{y_{2}-y_{1} }{x_{2}-x_{1}} = \frac{5-1 }{6-4} = \frac{4 }{2} = 2$ .

Let the -intercept be (0,b) . Then, using the slope and point (4,1) , we know that:

$m = \frac{y_{2}-y_{1} }{x_{2}-x_{1}} = \frac{b-1 }{0-4} = 2$

$2 =\frac{b-1 }{-4}$

$2 \cdot (-4) =\frac{b-1 }{-4} \cdot (-4)$

-8 =b-1

-8 + 1=b-1 + 1

-7 = b

The -intercept is (0,-7) .

Report an Error

Example Question #81 : Equations

Give the -intercept of the line of the equation: $\frac{}{}$ $\frac{2}{5}x + \frac{6}{7}y = 9$

Possible Answers:

$\left (0,3\frac{3}{5}\right )$

The line has no -intercept.

$\left (0,10\frac{1}{2}\right )$

$\left (0,22\frac{1}{2}\right )$

$\left (0,7\frac{5}{7}\right )$

Correct answer:

$\left (0,10\frac{1}{2}\right )$

Explanation:

Substitute x = 0 :

$\frac{2}{5}x + \frac{6}{7}y = 9$

$\frac{2}{5} \cdot 0 + \frac{6}{7}y = 9$

$0 + \frac{6}{7}y = 9$

$\frac{6}{7}y = 9$

$\frac{6}{7}y \cdot \frac{7}{6} = 9\cdot \frac{7}{6}$

$y = \frac{63}{6} = \frac{21}{2} = 10 \frac{1}{2}$

The -intercept is $\left (0,10\frac{1}{2}\right )$ .

Report an Error

Example Question #81 : Algebraic Concepts

Solve for , giving all real solutions:

$x^{6} - 7x^{3} -8 = 0$

Possible Answers:

$x = -\sqrt[3]{4} \textrm{ or } x =- \sqrt[3]{2} \textrm{ or } x = \sqrt[3]{2}\textrm{ or }x = \sqrt[3]{4}$

$x = -2 \textrm{ or }x = -1 \textrm{ or }x = 1 \textrm{ or } x = 2$

The equation has no real solution.

$x = - \sqrt[3]{2} \textrm{ or }x = \sqrt[3]{4}$

$x = -1 \textrm{ or }x = 2$

Correct answer:

$x = -1 \textrm{ or }x = 2$

Explanation:

Substitute $t = x^{3}$ and, subsequently, $t ^{2} =\left ( x^{3} \right )^{2} = x ^{6}$ .

$x^{6} - 7x^{3} -8 = 0$

$=t^{2} - 7t -8 = 0$

Factor as (t + ?) (t + ?) , replacing the two question marks with integers whose product is and whose sum is . These integers are -8,1 , so

(t -8) (t +1) = 0 .

Break this up into two equations, replacing $x^{3}$ for in each:

t -8 = 0

t = 8

$x ^{3}= 8$

$x = \sqrt[3]{8} = 2$

t+1= 0

t = -1

$x ^{3}= -1$

$x= \sqrt [3] {-1} = -1$

Report an Error

Example Question #87 : How To Find The Solution To An Equation

Give the -intercept of the line through points (-8,3) and (4,3) .

Possible Answers:

(4,0)

(-4,0)

The line has no -intercept.

(2,0)

(3,0)

Correct answer:

The line has no -intercept.

Explanation:

The slope of this line is

$m = \frac{y_{2}-y_{1} }{x_{2}-x_{1}} = \frac{3 -3 }{-8-4} = \frac{0 }{-12} = 0$ .

A line with slope 0 is horizontal, and therefore has no -intercept.

Report an Error

Example Question #781 : Isee Upper Level (Grades 9 12) Mathematics Achievement

y = 3x -8

x + 2y= 33

What is ?

Possible Answers:

x = 0

x = 49

x = 13

x = 7

x = -8

Correct answer:

x = 7

Explanation:

Substitute y = 3x -8 into the second equation:

x + 2y= 33

$x + 2 \left ( 3x -8 \right )= 33$

$x + 6x -16\right )= 33$

7x -16 = 33

7x -16 + 16 = 33+ 16

7x = 49

$7x \div 7= 49 \div 7$

x = 7

Report an Error

Example Question #89 : How To Find The Solution To An Equation

Solve for , giving all real solutions:

$4x^{2}+8x=140$

Possible Answers:

The equation has no real solutions.

$x \in \left \{ -7, 0, 5\right \}$

$x \in \left \{ -5, 7\right \}$

$x \in \left \{ -5, 0, 7\right \}$

$x \in \left \{ -7, 5\right \}$

Correct answer:

$x \in \left \{ -7, 5\right \}$

Explanation:

Write the equation in standard form:

$4x^{2}+8x=140$

$4x^{2}+8x - 140 =140 - 140$

$4x^{2}+8x - 140 =0$

can be factored out of each term:

$4 \cdot x^{2}+4 \cdot 2 x - 4 \cdot 35 =0$

$4 \left ( x^{2}+ 2 x - 35 \right ) =0$

Factor the trinomial by writing (x+?)(x+?) , replacing the question marks with two integers with product and sum . These integers are -5,7 , so the above becomes

4 (x+7)(x-5) =0 .

We can disregard the , as it does not contribute a solution. Set each of the other two factors equal to and solve separately:

$x + 7\Rightarrow x= -7$

$x - 5\Rightarrow x= 5$

The solution set is $\left \{ -7, 5\right \}$ .

Report an Error

Example Question #791 : Isee Upper Level (Grades 9 12) Mathematics Achievement

For what value of is $2^{x-3}=5$ ?

Possible Answers:

x=5.32

x=7.32

x=6

x=5

x=6.32

Correct answer:

x=5.32

Explanation:

We need to use logarithms.

$2^{x-3}=5\Rightarrow log\ 2^{x-3}=log\ 5$

$\Rightarrow (x-3)log\ 2= log\ 5$

$\Rightarrow x-3=\frac{log\ 5}{log\ 2}$

$\Rightarrow x=3+\frac{log\ 5}{log\ 2}$

$\Rightarrow x=3+2.32=5.32$

Report an Error

← Previous 1 2 … 5 6 7 8 9 10 11 12 13 … 18 19 Next →

View Tutors

Tynisha
Certified Tutor

Georgia State University, Bachelor in Arts, Political Science and Government. Thomas M Cooley Law School, Juris Doctor, Busin...

View Tutors

Jaroslaw
Certified Tutor

Heriot Watt University, Master of Science, Physics. Heriot Watt University, Doctor of Science, Theoretical and Mathematical P...

View Tutors

Joseph
Certified Tutor

University of Waterloo, Doctor of Philosophy, Applied Mathematics.

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GMAT Tutors in Dallas Fort Worth, Reading Tutors in Philadelphia, Chemistry Tutors in Washington DC, Spanish Tutors in Denver, ACT Tutors in San Francisco-Bay Area, Biology Tutors in Boston, SAT Tutors in Miami, GMAT Tutors in Chicago, SSAT Tutors in San Francisco-Bay Area, LSAT Tutors in New York City

Popular Courses & Classes

Spanish Courses & Classes in Philadelphia, MCAT Courses & Classes in San Diego, SAT Courses & Classes in Philadelphia, SAT Courses & Classes in Houston, GRE Courses & Classes in Miami, ACT Courses & Classes in Los Angeles, GRE Courses & Classes in Seattle, Spanish Courses & Classes in Washington DC, ISEE Courses & Classes in Los Angeles, SSAT Courses & Classes in Houston

Popular Test Prep

ISEE Test Prep in Atlanta, LSAT Test Prep in Chicago, GMAT Test Prep in Los Angeles, GMAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Phoenix, ISEE Test Prep in Boston, GRE Test Prep in Boston, SSAT Test Prep in Miami, ISEE Test Prep in Chicago, SSAT Test Prep in Houston

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

ISEE Upper Level Math : How to find the solution to an equation

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #81 : How To Find The Solution To An Equation

Example Question #82 : How To Find The Solution To An Equation

Example Question #83 : How To Find The Solution To An Equation

Example Question #84 : How To Find The Solution To An Equation

Example Question #81 : Equations

Example Question #81 : Algebraic Concepts

Example Question #87 : How To Find The Solution To An Equation

Example Question #781 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #89 : How To Find The Solution To An Equation

Example Question #791 : Isee Upper Level (Grades 9 12) Mathematics Achievement

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: