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

Example Question #151 : How To Find The Solution To An Equation

Solve for in this equation:

$\frac{5-2}{\sqrt{x}}=\frac{3}{4}$

Possible Answers:

Correct answer:

Explanation:

In order to solve for $\frac{5-2}{\sqrt{x}}=\frac{3}{4}$ , cross multiplication must be used. Applying this, the equestion to be solved will be:

$4(5-2)=3\sqrt{x}$

$4\cdot3=3\sqrt{x}$

Next, each side is divided by 3.

$4={\sqrt{x}}$

Next, each side is squared.

x=16

Report an Error

Example Question #152 : How To Find The Solution To An Equation

Solve for :

$x=\frac{125}{5x}$

Possible Answers:

$\pm 20$

$\pm 5$

Correct answer:

$\pm 5$

Explanation:

$x=\frac{125}{5x}$

The first step to solve for x is to multiply each side by 5x. This results in:

$5x^{2}=125$

Divide each side by 5.

$x^{2}=25$

Next, take the square root of each side. This results in:

$x=\pm 5$

Report an Error

Example Question #851 : Isee Upper Level (Grades 9 12) Mathematics Achievement

What is the solution to the equation 2(x-5)=3x+12 ?

Possible Answers:

x=11

x=-1

x=-22

x=22

x=-5

Correct answer:

x=-22

Explanation:

To start, use the distributive property on the left side: 2(x-5)=2x-10 , so that you then have 2x-10=3x+12 . Then, combine like terms to get 1x=-22 so that your final answer is x=-22.

Report an Error

Example Question #151 : Equations

Which of the following equations has as its solution set $\left \{ - 16, 20 \right \}$ ?

Possible Answers:

$\left | x - 5 \right | = 15$

$\left | x - 2 \right | = 18$

$\left | x - 3 \right | = 17$

$\left | x - 4 \right | = 16$

Correct answer:

$\left | x - 2 \right | = 18$

Explanation:

The absolute value of a nonnegative number is the number itself; the absolute value of a negative number is its positive opposite.

By substitution, 20 can be seen to be a solution of each of the equations in the four choices.

$\left | x - 2 \right | = 18$

$\left | 20 - 2 \right | = 18$

$\left |18 \right | = 18$ - true.

20 can be confirmed as a solution to the other three equations similarly. Therefore, the question is essentially to choose the equation with as a solution. Substituting for in each equation:

$\left | x - 2 \right | = 18$

$\left | -16 - 2 \right | = 18$

|-18| = 18 - true. This is the correct choice.

As for the other three:

$\left | -16 - 3 \right | = 17$

|-19| = 17

19 = 17 - false.

The other two equations can be similarly proved to not have as a solution.

Report an Error

Example Question #152 : Equations

$\frac{1}{x} = 12$

What is one tenth of ?

Possible Answers:

$1 \frac{1}{5}$

$\frac{5}{6}$

120

$\frac{1}{120}$

Correct answer:

$\frac{1}{120}$

Explanation:

$\frac{1}{x} = 12$ ; taking the reciprocal of both sides,

$x = \frac{1}{\left (\frac{1}{x} \right )} = \frac{1}{12}$

One tenth of is

$\frac{1}{10} \cdot x = \frac{1}{10} \cdot \frac{1}{12} = \frac{1}{120}$

Report an Error

Example Question #153 : Equations

$\frac{1}{x+2} = 12$

What is one sixth of ?

Possible Answers:

$12\frac{1}{2}$

$- \frac{23}{72}$

$- 11\frac{1}{2}$

$\frac{25}{72}$

Correct answer:

$- \frac{23}{72}$

Explanation:

Take the reciprocal of both sides of the equation, then solve:

$\frac{1}{x+2} = 12$

$x+2 = \frac{1}{12}$

$x+2 - 2 = \frac{1}{12} - 2$

$x = \frac{1}{12} - \frac{24}{12} = \frac{1-24}{12} = -\frac{23}{12}$

One sixth of this is

$\frac{1}{6} x = \frac{1}{6}\left ( -\frac{23}{12} \right ) = -\frac{23}{6 \cdot 12} = - \frac{23}{72}$

Report an Error

Example Question #151 : How To Find The Solution To An Equation

Give the solution set of the equation

$\left | 2x- 7\right | + 49 = 20$

Possible Answers:

The set of all real numbers

The equation has no solution

$\left \{ 11, 18\right \}$

$\left \{ -18, -11 \right \}$

Correct answer:

The equation has no solution

Explanation:

$\left | 2x- 7\right | + 49 = 20$

$\left | 2x- 7\right | + 49 - 49 = 20 - 49$

$\left | 2x- 7\right | = -29$

Since it is impossible for the absolute value of a number to be negative, the equation has no solution.

Report an Error

Example Question #152 : Equations

How many real solutions does the equation

$8x^{3} + 12x^{2} = 18 x + 27$

have?

Possible Answers:

Three

None

One

Two

Correct answer:

Two

Explanation:

$8x^{3} + 12x^{2} = 18 x + 27$

$8x^{3} + 12x^{2} - 18 x - 27 = 18 x + 27 - 18 x - 27$

$8x^{3} - 18 x + 12x^{2}- 27 = 0$

$(8x^{3} - 18 x )+ (12x^{2}- 27) = 0$

$2x (4x^{2} - 9 )+ 3 (4x^{2}- 9) = 0$

$(2x + 3 )(4x^{2} - 9 ) = 0$

$(2x + 3 ) [ (2x)^{2} - 3^{2} ]= 0$

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

One of two things must happen - either

2x+3 = 0

2x-3 = 0

This gives this equation two real solutions - the solutions to these two equations.

Report an Error

Example Question #154 : Equations

Give the solution set of the equation

' $12x^{2} + 26x = 56$

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

$12x^{2} + 26x = 56$

$12x^{2} + 26x - 56 = 56 - 56$

$12x^{2} + 26x - 56 = 0$

$2 (6x^{2} + 13x - 28 ) = 0$

The quadratic trinomial can be factored using the method by looking for two integers whose sum is 13 and whose product is $6 \times (-28 ) = -168$ . Throught trial and error, we see that these integers are and 21, so we continue:

$2 (6x^{2} -8x+21 x - 28 ) = 0$

$2\left [ (6x^{2} -8x)+( 21 x - 28 ) \right ]= 0$

$2\left [2x (3x -4)+7( 3x - 4) \right ]= 0$

2(2x+7)(3x-4) = 0

One of the factors must be equal to 0, so either:

2x+7 = 0

2x = -7

$x = -\frac{7}{2} = -3\frac{1}{2}$

3x-4 = 0

3x = 4

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

The correct choice is $\left \{ -3\frac{1}{2}, 1 \frac{1}{3 } \right \}$ .

Report an Error

Example Question #152 : Equations

List all real solutions of the equation

$x^{3}+4x^{2}= 16x+ 64$

Possible Answers:

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

$\left \{ 4\right \}$

No real solutions

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

Correct answer:

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

Explanation:

$x^{3}+4x^{2}= 16x+ 64$

$x^{3}+4x^{2} - 16x - 64 = 16x+ 64 - 16x - 64$

$x^{3}+4x^{2} - 16x - 64 = 0$

$(x^{3}+4x^{2} )- (16x + 64 )= 0$

$x^{2} (x + 4 )- 16 (x + 4 )= 0$

$(x^{2} - 16) (x + 4 )= 0$

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

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

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

By the Zero Product Principle:

x- 4 = 0 , in which case x = 4 ,

x+ 4 = 0 , in which case x = -4 .

The correct choice is $\left \{ -4, 4\right \}$ .

Report an Error

View Tutors

Reza
Certified Tutor

University of Sherbrooke, Doctor of Philosophy, Mathematics. University of Manitoba, Master of Science, Mathematics.

View Tutors

Gabby
Certified Tutor

University of Oregon, Bachelor in Arts, Journalism. University of Oregon, Current Grad Student, Communication, General.

View Tutors

Ana
Certified Tutor

Grand Canyon University, Bachelors, Education. Grand Canyon University, Masters, Education.

All ISEE Upper Level Math Resources

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

Popular Subjects

ACT Tutors in Seattle, French Tutors in San Francisco-Bay Area, Statistics Tutors in Atlanta, Spanish Tutors in Dallas Fort Worth, English Tutors in Chicago, Physics Tutors in New York City, Statistics Tutors in Philadelphia, MCAT Tutors in Boston, GRE Tutors in Atlanta, Chemistry Tutors in Chicago

Popular Courses & Classes

Spanish Courses & Classes in Seattle, GRE Courses & Classes in San Diego, ISEE Courses & Classes in Houston, SSAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Chicago, SSAT Courses & Classes in Philadelphia, GRE Courses & Classes in Boston, ISEE Courses & Classes in Seattle, LSAT Courses & Classes in Philadelphia, GMAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

GRE Test Prep in San Diego, ACT Test Prep in New York City, SSAT Test Prep in New York City, GRE Test Prep in Houston, LSAT Test Prep in Boston, ISEE Test Prep in New York City, ACT Test Prep in Chicago, LSAT Test Prep in Philadelphia, GMAT Test Prep in Chicago, GRE Test Prep in New York City

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 #151 : How To Find The Solution To An Equation

Example Question #152 : How To Find The Solution To An Equation

Example Question #851 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #151 : Equations

Example Question #152 : Equations

Example Question #153 : Equations

Example Question #151 : How To Find The Solution To An Equation

Example Question #152 : Equations

Example Question #154 : Equations

Example Question #152 : Equations

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: