Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : 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 #1 : Inequalities

Given that x = 2 and y = 4, how much less is the value of 2x² – 2y than the value of 2y² – 2x ?

Possible Answers:

Correct answer:

Explanation:

First, we solve each expression by plugging in the given values for x and y:

2(2²) – 2(4) = 8 – 8 = 0

2(4²) – 2(2) = 32 – 4 = 28

Then we find the difference between the first and second expressions’ values:

28 – 0 = 28

Report an Error

Example Question #2 : Inequalities

Solve | z + 5 | > 2

Possible Answers:

z < 2

2 < z < 5

-7 < z < -3

$z > -3 \; or\; z < -7$

z > 5

Correct answer:

$z > -3 \; or\; z < -7$

Explanation:

Absolute value problems are broken into two inequalities: z + 5 > 2 and z + 5 < -2 . Each inequality is solved separately to get z > -3 and z < -7 . Graphing each inequality shows that the correct answer is $z > -3\; OR\; z < -7$ .

Report an Error

Example Question #3 : Inequalities

Which of the following inequalities defines the solution set to $3x+1\leq-4x-6$ ?

Possible Answers:

$x\leq-1$

$x\geq1$

$x\leq1$

$x\geq-1$

$x\leq-7$

Correct answer:

$x\leq-1$

Explanation:

First, move the s to one side.

$7x+1\leq-6$

Subtract by 1

$7x\leq-7$

Divide both sides by 7.

$x\leq-1$

Report an Error

Example Question #5 : Inequalities

The cost, in cents, of manufacturing $\dpi{100} \small x$ pencils is $\dpi{100} \small 1200+20x$ , where 1200 is the number of cents required to run the factory regardless of the number of pencils made, and 20 represents the per-unit cost, in cents, of making each pencil. The pencils sell for 50 cents each. What number of pencils would need to be sold so that the revenue received is at least equal to the manufacturing cost?

Possible Answers:

$\dpi{100} \small 40$

$\dpi{100} \small 30$

$\dpi{100} \small 33$

$\dpi{100} \small 36$

$\dpi{100} \small 27$

Correct answer:

$\dpi{100} \small 40$

Explanation:

If each pencil sells at 50 cents, $\dpi{100} \small x$ pencils will sell at $\dpi{100} \small 50x$ . The smallest value of $\dpi{100} \small x$ such that

$\dpi{100} \small 50x\geq 1200+20x$

$\dpi{100} \small x\geq 40$

Report an Error

Example Question #4 : How To Find The Solution To An Inequality With Subtraction

Solve the following inequality:

x-2<13

Possible Answers:

x<11

x>15

x<15

x>11

Correct answer:

x<15

Explanation:

To solve an inequality with subtraction, simply solve it is as an equation.

The goal is to isolate the variable on one side with all other constants on the other side. Perform the opposite operation to manipulate the inequality.

In this case add two to each side.

x-2<13

x-2=13

x=15

x<15

Report an Error

Example Question #4 : Inequalities

Solve the following inequality:

3x-7<5

Possible Answers:

x>4

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

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

x<4

Correct answer:

x<4

Explanation:

To solve, simply treat it as an equation.

This means you want to isolate the variable on one side and move all other constants to the other side through opposite operation manipulation.

Remember, you only flip the inequality sign if you multiply or divide by a negative number.

Thus,

$3x-7<5\Rightarrow 3x<12\Rightarrow x<4$

Report an Error

Example Question #4 : Inequalities

Solve |x – 5| ≤ 1

Possible Answers:

-1 ≤ x ≤ 1

x ≤ 4 or x ≥ 6

None of the answers are correct

4 ≤ x ≤ 6

0 ≤ x ≤ 1

Correct answer:

4 ≤ x ≤ 6

Explanation:

Absolute values have two answers: a positive one and a negative one. Therefore,

-1 ≤ x – 5≤ 1 and solve by adding 5 to all sides to get 4 ≤ x ≤ 6.

Report an Error

Example Question #5 : Inequalities

Solve $|z - 3| \leq 5$

Possible Answers:

$z \leq 8$

$-2 \geq z$

$-2 \leq z \leq 8$

No solutions

All real numbers

Correct answer:

$-2 \leq z \leq 8$

Explanation:

Absolute value is the distance from the origin and is always positive.

So we need to solve $z - 3 \leq 5$ and $z - 3 \geq -5$ which becomes a bounded solution.

Adding 3 to both sides of the inequality gives $z \leq 8$ and $z \geq -2$ or in simplified form $-2 \leq z\leq 8$

Report an Error

Example Question #5 : Inequalities

Given the inequality $\left | 12-2x\right |>2,$ which of the following is correct?

Possible Answers:

x<5 or x>7

x<-5 or x>7

5<x<7

x<-7 or x>5

-5<x<7

Correct answer:

x<5 or x>7

Explanation:

First separate the inequality $\left | 12-2x\right |>2$ into two equations.

12-2x>2

12-2x<-2

Solve the first inequality.

12-2x>2

-2x>-10

x<5

Solve the second inequality.

12-2x<-2

-2x<-14

x>7

Thus, x<5 or x>7 .

Report an Error

Example Question #11 : Inequalities

What values of x make the following statement true?

|x – 3| < 9

Possible Answers:

6 < x < 12

–6 < x < 12

–3 < x < 9

–12 < x < 6

x < 12

Correct answer:

–6 < x < 12

Explanation:

Solve the inequality by adding 3 to both sides to get x < 12. Since it is absolute value, x – 3 > –9 must also be solved by adding 3 to both sides so: x > –6 so combined.

Report an Error

View ACT Math Tutors

Alejandro
Certified Tutor

Kennesaw State University, Bachelor of Science, Computer Software Engineering.

View ACT Math Tutors

Lauren
Certified Tutor

University of Mississippi, Masters in Education, Education.

View ACT Math Tutors

Mark
Certified Tutor

Murray State University, Bachelor of Science, Mathematics.

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

Spanish Courses & Classes in Miami, SAT Courses & Classes in New York City, Spanish Courses & Classes in Los Angeles, Spanish Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in San Diego, ISEE Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Phoenix, SAT Courses & Classes in Chicago, LSAT Courses & Classes in Houston

Popular Test Prep

LSAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Houston, SAT Test Prep in Los Angeles, LSAT Test Prep in Phoenix, GRE Test Prep in San Diego, ACT Test Prep in Seattle, SSAT Test Prep in Dallas Fort Worth, ACT Test Prep in Phoenix, MCAT Test Prep in Chicago, ISEE 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)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

ACT Math : Inequalities

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Inequalities

Example Question #2 : Inequalities

Example Question #3 : Inequalities

Example Question #5 : Inequalities

Example Question #4 : How To Find The Solution To An Inequality With Subtraction

Example Question #4 : Inequalities

Example Question #4 : Inequalities

Example Question #5 : Inequalities

Example Question #5 : Inequalities

Example Question #11 : Inequalities

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: