Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Equations / Inequalities

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #84 : Algebra

Translate into an algebraic expression:

Two fifths of the difference of five times a number and two equals six times the number.

Possible Answers:

$\frac{2}{5}(2x+5)=6x$

$\frac{2}{5}(5x-2)=6x$

$\frac{2}{5}(2x-5)=6x$

$\frac{2}{5}(2-5x)=6x$

$\frac{2}{5}(5x+2)=6x$

Correct answer:

$\frac{2}{5}(5x-2)=6x$

Explanation:

In order to translate the description into an algebraic expression, you must first form the difference (5x-2) , multiply it by $\frac{2}{5}$ , and then set the equation equal to , as follows:

$\frac{2}{5}(5x-2)=6x$

Report an Error

Example Question #121 : How To Find The Solution To An Equation

A car averages miles per gallon. If gas costs $\$ 3.04$ per gallon, which of the following is closest to how much the gas would cost for this car to travel $1\textup{,}642$ typical miles?

Possible Answers:

$\$51$

$\$155$

$\$156$

$\$50$

$\$17$

Correct answer:

$\$156$

Explanation:

To solve this problem you should divide the total number of miles $\left ( 1\textup{,}642\right )$ by the miles per gallon $\left ( 32\right )$ , and then multiply by the cost of gas per gallon $\left ( \$3.04\right )$ . This gives you $\$155.99$ , which is closest to $\$156$ .

Report an Error

Example Question #121 : Equations / Inequalities

When $\textup{w}= 6\textup{ and } \textup{z} = 4$ , by how much does the value of $3\textup{w}^{2}-2\textup{z}$ exceed the value of $2\textup{w}^{2} - 3\textup{z}$ ?

Possible Answers:

Correct answer:

Explanation:

You must plug in for $\textup{w}$ and for $\textup{z}$ , this means $3\textup{w}^{2}-2\textup{z}=$ $3\left ( 36\right )-2\left ( 4\right )=100$ and $2\textup{w}^{2}-3\textup{z}=2\left ( 36\right )-3\left ( 4\right )=60$

100-60=40

Report an Error

Example Question #122 : How To Find The Solution To An Equation

What is the value of $\textup{t}$ when $3\textup{t}+5=7\textup{t}-2$ ?

Possible Answers:

$\frac{7}{10}$

$\frac{4}{7}$

$\frac{7}{4}$

$\frac{4}{3}$

$\frac{3}{4}$

Correct answer:

$\frac{7}{4}$

Explanation:

The first step is to subtract $\textup{3t}$ from both sides so you're left with $5=4\textup{t}-2$ . Next, you add to both sides, giving you $7=4\textup{t}$ . The final step is to divide by , giving you $\frac{7}{4}=\textup{t}$ .

Report an Error

Example Question #123 : How To Find The Solution To An Equation

Karen has $\$7$ more than times as many dollars as Susan. Karen also has $\frac{1}{2}$ as many dollars as John would if he had more dollars. How many dollars does Susan have, relative to John?

Possible Answers:

$\frac{J}{4}$

$\frac{J-12}{6}$

3J -3

J + 2

6J -4

Correct answer:

$\frac{J-12}{6}$

Explanation:

First, set up our two equations. If Karen has seven dollars more than three times as many dollars as Susan, then K = 3S +7 . If Karen has half as many dollars as John would if he had two more dollars, then $K = \frac{J+2}{2}$ . The Substitution Property of Equality thus says that $3S +7 = \frac{J+2}{2}$ . Now, we simply solve for in terms of .

$3S +7 = \frac{J+2}{2}$

6S +14 = J+2

6S = J-12

$S = \frac{J-12}{6}$

Report an Error

Example Question #121 : How To Find The Solution To An Equation

If the third day of the year is a Wednesday, what is the 165th day?

Possible Answers:

Thursday

Monday

Wednesday

Friday

Tuesday

Correct answer:

Thursday

Explanation:

If the third day is a Wednesday, then the first day is a Monday. 23 weeks will complete a cycle with the 161st day. Therefore, the fourth day past that, 165, is a Thursday.

Report an Error

Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

John, Jill, and Jack are splitting a pizza. John eats 1/2 of the pizza and Jill eats 1/3 of the pizza. How much of the pizza is left for Jack?

Possible Answers:

3/5

1/6

1/5

1/3

None

Correct answer:

1/6

Explanation:

We can write an equation for the amount of pizza eaten, with as the amount left for Jack.

$\frac{1}{2} + \frac{1}{3} + x = 1$

To solve this equation, we must find the lowest common denominator of 1/2 and 1/3 . We can list the multiples of and to find the least common multiple:

2: 2, 4, 6, 8, 10, 12, ...

3: 3, 6, 12, 15, 18, 21, ...

We can see that the least common multiple of and is , so we can rewrite each of the fractions with a denominator of .

$\frac{1}{2}\cdot \frac{3}{3} = \frac{3}{6}$

$\frac{1}{3}\cdot \frac{2}{2} = \frac{2}{6}$

When we put these fractions back into the equation, we can solve for :

$\frac{3}{6} + \frac{2}{6} + x = 1$

$\frac{5}{6} + x = 1$

$x = \frac{1}{6}$

Report an Error

Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

What is the slope of a line represented by the equation:

15y + 3x = 4

Possible Answers:

$\frac{4}{3}$

$\frac{3}{4}$

$-\frac{1}{5}$

$\frac{1}{5}$

Correct answer:

$-\frac{1}{5}$

Explanation:

To solve problems where you need to find the slope of a line in a given equation, change the equation so that it matches y-intercept form:

y=mx+b

For this equation, first move the 3x over to the other side of the equation.

15y + 3x = 4

-3x -3x

The equation should now look like this:

15y = -3x + 4

Then, divide by 15 to isolate the variable .

$\frac{15y}{15} =-\frac{3x}{15} + \frac{4}{15} \rightarrow y =-\frac{3}{15}x + \frac{4}{15}$

Then simplify

$y =-\frac{3}{15}x + \frac{4}{15} \rightarrow y =-\frac{1}{5}x + \frac{4}{15}$

Whatever number is before the x in the equation (m) is your slope.

$-\frac{1}{5}$

Report an Error

Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

Rational_5

Possible Answers:

–1

–2

Correct answer:

Explanation:

Rational_2

Rational_3

Rational_4

Report an Error

Example Question #2 : How To Find The Solution To A Rational Equation With Lcd

Linesmb1

Possible Answers:

b/(m²+ 1)

–bm/(m²+ 1)

bm/(m²+ 1)

–b/(m + 1)

–b/(m²– 1)

Correct answer:

b/(m²+ 1)

Explanation:

Linesmb5

Linesmb4

Report an Error

View ACT Math Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

View ACT Math Tutors

Bibhash
Certified Tutor

Pune University, Bachelor in Arts, Ecommerce. SDA Bocconi School of Management, Masters in Business Administration, Finance.

View ACT Math Tutors

Quang
Certified Tutor

Georgetown University, Bachelor of Science, Finance.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

ACT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Phoenix, LSAT Courses & Classes in Denver, MCAT Courses & Classes in Miami, GMAT Courses & Classes in Denver, MCAT Courses & Classes in Atlanta, MCAT Courses & Classes in Boston, SAT Courses & Classes in Boston, ACT Courses & Classes in Miami, GRE Courses & Classes in San Francisco-Bay Area

Popular Test Prep

LSAT Test Prep in Miami, ACT Test Prep in Los Angeles, ACT Test Prep in Philadelphia, GMAT Test Prep in Seattle, GRE Test Prep in Los Angeles, GMAT Test Prep in Denver, SAT Test Prep in Boston, SSAT Test Prep in Dallas Fort Worth, ACT Test Prep in Washington DC, ACT 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

ACT Math : Equations / Inequalities

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #84 : Algebra

Example Question #121 : How To Find The Solution To An Equation

Example Question #121 : Equations / Inequalities

Example Question #122 : How To Find The Solution To An Equation

Example Question #123 : How To Find The Solution To An Equation

Example Question #121 : How To Find The Solution To An Equation

Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

Example Question #2 : How To Find The Solution To A Rational Equation With Lcd

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: