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 #171 : Algebraic Concepts

Define $f (x) = x^{2}$ .

If (fg)(2) = 64 , which of the following cannot be a valid definition of ?

Possible Answers:

$g(x) = x ^{3}$

$g(x) = \frac{32}{x}$

$g(x) = x^{2} + 12$

g(x) = 8x

Correct answer:

$g(x) = x ^{3}$

Explanation:

$f (x) = x^{2}$ , so, substituting 2 for , we see that

$f (2) = 2^{2} =4$ .

By definition,

$(fg)(2) = f(2) \cdot g(2)$ , so

(fg)(2) = 64

Substituting and solving for g(2) :

$f(2) \cdot g(2) = 64$

$4\cdot g(2) = 64$

$4\cdot g(2) \div 4 = 64 \div 4$

g(2) = 16

Examine all four alternatives by, again, substituting 2 for in each and finding for which one $g(2) \ne 16$ :

$g(x) = x^{2} + 12$

$g(2) = 2^{2} + 12 = 4 + 12 = 16$

$g(x) = \frac{32}{x}$

$g(2) = \frac{32}{2} = 16$

g(x) = 8x

$g(2) = 8 \cdot 2 = 16$

$g(x) = x ^{3}$

$g(2) = 2 ^{3} = 8$

Therefore, of the four choices, only $g(x) = x ^{3}$ is not a valid definition, since it does not match the conditions.

Report an Error

Example Question #171 : Equations

Define $f(x) = x^{5}$ .

If $\frac{f}{g} (5) = 50$ , then which of the following could be the definition of g(x) ?

Possible Answers:

$g(x) =\frac{ x^{3}}{2}$

$g(x) = 2x^{3}$

$g(x) =\frac{2}{ x^{3}}$

$g(x) =\frac{1}{ 2x^{3}}$

Correct answer:

$g(x) =\frac{ x^{3}}{2}$

Explanation:

By definition,

$\frac{f}{g} (5) = \frac{f(5)}{g(5)}$ .

Also, by substitution:

$f(x) = x^{5}$

$f(5) = 5^{5} = 3,125$

Therefore, the question is equivalent to asking for which definition of g(x) it holds that

$\frac{3,125}{g(5)} = 50$

Each definition in the given choices can be evaluated for x = 5 by substitution, with each value of g(5) tested in turn:

$g(x) =\frac{1}{ 2x^{3}}$

$g(5) =\frac{1}{ 2 \cdot 5^{3}} = \frac{1}{ 2 \cdot 125} = \frac{1}{250} = 0.004$

$\frac{f}{g} (5) = \frac{3,125}{0.008} = 3,125 \div 0.008 = 390,625$

$g(x) =\frac{2}{ x^{3}}$

$g(x) =\frac{2}{ 5^{3}}= \frac{2}{125} = 0.016$

$\frac{f}{g} (5) = \frac{3,125}{0.016} = 3,125 \div 0.016 =195, 312 .5$

$g(x) = 2x^{3}$

$g(5) = 2 \cdot 5^{3} = 2 \cdot 125 = 250$

$\frac{f}{g} (5) = \frac{3,125}{250} = 12.5$

$g(x) =\frac{ x^{3}}{2}$

$g(x) =\frac{ 5^{3}}{2} = \frac{ 125}{2} = 62.5$

$\frac{f}{g} (5) = \frac{3,125}{62.5} = 50$

This makes $g(x) =\frac{ x^{3}}{2}$ the correct choice.

Report an Error

Example Question #172 : Equations

Define f (x) = 7x - 23 .

If (f-g) (8) = 34 , then which of the following could be a valid definition of the function ?

Possible Answers:

g(x) = x - 6

g(x) = x - 7

g(x) = x - 9

g(x) = x- 8

Correct answer:

g(x) = x - 9

Explanation:

f (x) = 7x - 23 , so, substituting 8 for , we see that

$f (8) = 7 \cdot 8 - 23= 56 - 23 = 33$

By definition,

(f-g) (8) = f(8) - g (8) , so

(f-g) (8) = 34

f(8) - g (8) = 34

33 - g (8) = 34

33 - g (8) - 33 = 34 - 33

-g(8)= 1

g(8) = -1

Examine all four alternatives by, again, substituting 8 for , and find the one for which g(8) = -1 .

g(x) = x - 6

g(x) = 8 - 6 = 2

g(x) = x - 7

g(x) = 8 - 7 = 1

g(x) = x- 8

g(x) = 8- 8 = 0

g(x) = x - 9

g(x) = 8 - 9 = -1

Of the four choices, g(x) = x - 9 is the definition such that g(8) = -1 .

Report an Error

Example Question #172 : Algebraic Concepts

Solve the following equation for t, when d is 6.

5t^2=6d+34

Possible Answers:

t=70

$t=\pm\sqrt{14}$

$t=\sqrt{14}$

t=14

Correct answer:

$t=\pm\sqrt{14}$

Explanation:

Solve the following equation for t, when d is 6.

5t^2=6d+34

Let's begin by plugging 6 in for d and then, using algebra, we will find t.

5t^2=6(6)+34

5t^2=36+34

5t^2=70

Divide by 5:

$t^2=\frac{70}{5}=14$

Square root both sides to finish up

$t=\sqrt{14}$

Almost there, but because we are square rooting, we need plus or minus the square root of 14

$t=\pm\sqrt{14}$

The reason for this is that positive or negative square root of 14 will get us positive 14 when we square it. Therefore, we technically have two answers.

Report an Error

Example Question #173 : Algebraic Concepts

Which solution makes this equation true:

5x-8=12

Possible Answers:

x=7

x=5

x=4

x=15

x=3

Correct answer:

x=4

Explanation:

To solve for x, we want x to stand alone. So, we get

5x-8=12

5x-8+8=12+8

5x-0=20

5x=20

$\frac{5x}{5} = \frac{20}{5}$

x=4

Report an Error

Example Question #171 : Equations

Solve the following equation when y is equal to 12.

$\sqrt{y^2}-4=c^3$

Possible Answers:

c=12

c=-2

c=2

Not enough information provided.

Correct answer:

c=2

Explanation:

Solve the following equation when y is equal to 12.

$\sqrt{y^2}-4=c^3$

To begin, let's realize that

$\sqrt{y^2}=y$

So, let's update our original equation.

y-4=c^3

Now, let's plug in 12 for y

12-4=c^3

8=c^3

So, what number cubed equals 8?

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

So our answer is 2

Report an Error

Example Question #171 : Equations

Solve the following equation for q.

3q^3-147=12

Possible Answers:

$q=\sqrt{53}$

$q=\sqrt[3]{45}$

$q=\sqrt[3]{53}$

$q=\sqrt[3]{59}$

Correct answer:

$q=\sqrt[3]{53}$

Explanation:

Solve the following equation for q.

3q^3-147=12

First, let's divide everything by three. This will work because 147 and 12 are both divisible by 3

$(3q^3-147=12)\div3\rightarrow q^3-49=4$

Now, add 49 to both sides to get the variable by itself

q^3=53

$q=\sqrt[3]{53}$

Now, this doesn't come out to a neat decimal, so we will just leave it as is.

Report an Error

Example Question #172 : Equations

Which of the following makes this equation true:

7y-13=29

Possible Answers:

y=9

y=7

y=2

y=8

y=6

Correct answer:

y=6

Explanation:

To answer the question, we will need to solve for y. We get

7y-13=29

7y-13+13=29+13

7y-0=42

7y=42

$\frac{7y}{7} = \frac{42}{7}$

y=6

Report an Error

Example Question #176 : Algebraic Concepts

Solve the following equation for j.

14j-12=58

Possible Answers:

j=2

No real solutions

j=-5

j=5

Correct answer:

j=5

Explanation:

Solve the following equation for j.

14j-12=58

We can solve this with basic algebra.

First, add 12 to both sides:

14j-12(+12)=58(+12)

14j=70

Next, divide both sides by 14

$14j\div14=70 \div 14$

$j=\frac{70}{14}=5$

And we end up with...

j=5

Report an Error

Example Question #177 : Algebraic Concepts

Which of the following makes the equation true:

$\frac{x}{5} +9 = 12$

Possible Answers:

x=7

x=12

x=15

x=5

x=3

Correct answer:

x=15

Explanation:

To find the answer, we will solve for x. So, we get

$\frac{x}{5} +9 = 12$

$\frac{x}{5} +9 -9 = 12-9$

$\frac{x}{5} + 0 = 3$

$\frac{x}{5} = 3$

$\frac{x}{5} \cdot 5 = 3 \cdot 5$

x=15

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

LSAT Tutors in Los Angeles, Biology Tutors in New York City, Reading Tutors in Chicago, Statistics Tutors in Atlanta, MCAT Tutors in Washington DC, ISEE Tutors in Washington DC, Biology Tutors in Miami, MCAT Tutors in Miami, GMAT Tutors in Houston, GMAT Tutors in Los Angeles

Popular Courses & Classes

GRE Courses & Classes in Boston, GMAT Courses & Classes in Chicago, SSAT Courses & Classes in New York City, ACT Courses & Classes in San Diego, GMAT Courses & Classes in New York City, GRE Courses & Classes in Seattle, Spanish Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Houston

Popular Test Prep

GMAT Test Prep in Los Angeles, SSAT Test Prep in Philadelphia, MCAT Test Prep in New York City, MCAT Test Prep in Atlanta, LSAT Test Prep in Houston, ACT Test Prep in Boston, SAT Test Prep in Boston, GMAT Test Prep in Chicago, SSAT Test Prep in New York City, SAT Test Prep in Denver

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 #171 : Algebraic Concepts

Example Question #171 : Equations

Example Question #172 : Equations

Example Question #172 : Algebraic Concepts

Example Question #173 : Algebraic Concepts

Example Question #171 : Equations

Example Question #171 : Equations

Example Question #172 : Equations

Example Question #176 : Algebraic Concepts

Example Question #177 : Algebraic Concepts

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: