We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Solving Inequalities

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 7 8 9 10 11 12 Next →

Example Question #1 : Solving Inequalities

Solve for .

$-7x-4\geq10$

Possible Answers:

$x\geq-2$

$x\leq-2$

$x\leq2$

$x\geq2$

Correct answer:

$x\leq-2$

Explanation:

$-7x-4\geq10$

Add 4 to both sides.

$-7x\geq14$

Divide both sides by –7. When dividing by a negative value, we must also change the direction of the inequality sign.

$x\leq-2$

Report an Error

Example Question #1 : Solving Inequalities

Solve this inequality.

$\left | \frac{4x+3}{x+6}\right |\eq>1$

Possible Answers:

$x\eq>-\frac{9}{5}, x \eq<1$

$x\eq>-\frac{9}{5}, x\eq>1$

$x\eq<\frac{9}{5}, x\eq>-1$

$x \eq< -\frac{9}{5}, \hspace x \eq>1$

$x<-\frac{9}{5}, x\eq<1$

Correct answer:

$x \eq< -\frac{9}{5}, \hspace x \eq>1$

Explanation:

Split the inequality into two possible cases as follows, based on the absolute values.

First case: $\frac{4x+3}{x+6}\eq>1$

Second case: $\frac{4x+3}{x+6} \eq< -1$

Let's find the inequality of the first case.

$\frac{4x+3}{x+6} \eq>1$

Multiply both sides by x + 6.

$4x+3 \eq>x+6$

Subtract x from both sides, then subtract 3 from both sides.

$3x \eq>3$

Divide both sides by 3.

$x\eq>1$

Let's find the inequality of the second case.

$\frac{4x+3}{x+6} \eq< -1$

Multiply both sides by x + 6.

$4x+3 \eq< -1(x+6)$

Simplify.

4x+3< -x-6

Add x to both sides, then subtract 3 from both sides.

$5x\eq< -9$

Divide both sides by 5.

$x \eq<-\frac{9}{5}$

So the range of x-values is $x<-\frac{9}{5}$ and $x \eq>1$ .

Report an Error

Example Question #1 : Graphing Inequalities

Solve the compound inequality and express answer in interval notation:

$\small x-3 > -1$ or $\small x+2 < 4$

Possible Answers:

$\small (-\infty , 2) \cup \left (2, \infty \right )$

$\small \varnothing$ (no solution)

$\small \left (-\infty, \infty \right )$

$\small (2,2)$

Correct answer:

$\small (-\infty , 2) \cup \left (2, \infty \right )$

Explanation:

For a compound inequality, we solve each inequality individually. Thus, for the first inequality, $\small x-3 > -1$ , we obtain the solution x>2 and for the second inequality, $\small x+2 < 4$ , we obtain the solution x<2 . In interval notation, the solutions are $\small (2, \infty)$ and $\small (-\infty, 2)$ , respectively. Because our compound inequality has the word "or", this means we union the two solutions to obatin $\small (-\infty , 2) \cup \left (2, \infty \right )$ .

Report an Error

Example Question #1 : Solving Inequalities

Find the solution set of the inequality:

$6x + 22 \leq 97$

Possible Answers:

$[12.5, \infty)$

$\left ( -\infty , \infty \right )$

$(-\infty , -12.5]$

$(-\infty , 12.5]$

$[-12.5, \infty)$

Correct answer:

$(-\infty , 12.5]$

Explanation:

$6x + 22 \leq 97$

$6x + 22 -22 \leq 97-22$

$6x \leq 75$

$6x \div 6 \leq 75\div 6$

$x \leq 12.5$

or, in interval notation, $(-\infty , 12.5]$

Report an Error

Example Question #1 : Solving Inequalities

Sam's age is three years more than twice his brother's age. If the sum of their ages is at least 18, then was is the maximum possible age of Sam's brother?

Possible Answers:

years old

Correct answer:

years old

Explanation:

Let be Sam's age, and let be his brother's age.

In the problem, we are told that the sum of their ages is at least 18. Represent this with an inequality:

$x+y\leq 18$

Sam's age is three years more than twice his brothers age. Write this mathematically as:

2y+3=x

Plug in 2y+3 for the value in the inequality and solve for :

$2y+3+y\leq 18$

$3y+3\leq 18$

$3y\leq 15$

$y\leq 5$

The age of Sam's brother is less than or equal to years.

Report an Error

Example Question #4 : Solving Inequalities

Solve the inequality:

$\small x^2+4< 9$

Possible Answers:

$\small -\sqrt5> x\ or\ x> \sqrt5$

$\small x< -\sqrt5$

$\small -\sqrt5< x< \sqrt5$

$\small x< \sqrt5$

Correct answer:

$\small -\sqrt5< x< \sqrt5$

Explanation:

$\small \small x^2+4< 9$

$\small x^2< 5$

$\small x< \left | (\pm\sqrt5) \right |$

$\small -\sqrt5< x< \sqrt5$

Report an Error

Example Question #5 : Solving Inequalities

Solve the following inequality for :

$\large -7x-2 \ge 12$

Possible Answers:

$\large x \ge 2$

$\large x \ge -2$

x > -10/7

$x \le -2$

Correct answer:

$x \le -2$

Explanation:

Most of solving inequalities is straightforward algebra and we can manipulate them in the same way as equations in most cases.

$\large -7x-2 \ge 12$

$\large -7x \ge 14$

However, we must remember that when multiplying or dividing by negative numbers in inequalities, we have to switch the direction of the inequality. So we do the final division step and get the answer:

$\large x \le -2$

Report an Error

Example Question #6 : Solving Inequalities

Solve for :

$3x+20\leq -5x-4$

Possible Answers:

x < -3

$x \leq 3$

$x \geq -3$

$x \geq 3$

$x \leq -3$

Correct answer:

$x \leq -3$

Explanation:

In order to solve this inequality, we must first consolidate all of our values on one side.

The first thing we need to do is move the to the other side:

$3x+\underset{-20}{20} \le -5x - \underset{-20}{4}$

This results in:

$3x \le -5x-24$

Next, we need to move the -5x from the right side over to the left side:

$\underset{+5x}{3x} \le \underset{+5x}{-5x}-24$

This gives us

$8x \le -24$

Dividing each side by gives us our solution:

$x \le -3$

Report an Error

Example Question #7 : Solving Inequalities

What are the possible values of if 2x+7>5 and 3x-7<2x ?

Possible Answers:

-1<x<7

0<x<9

x=8

x<7

Correct answer:

-1<x<7

Explanation:

The two equations should be solved separately to get,

2x+7>5

2x>-2

x>-1 and

3x-7<2x

x<7 .

This can be checked by plugging in values between and and seeing if they satisfy both equations.

Report an Error

Example Question #1 : Solving Inequalities

Find the solution set of the inequality:

6x + 22 > 67

Possible Answers:

$\left ( - \infty, -7.5 \right )$

$\left ( - \infty, 7.5 \right )$

$\left ( -\infty , \infty \right )$

$\left ( 7.5, \infty \right )$

$\left ( -7.5, \infty \right )$

Correct answer:

$\left ( 7.5, \infty \right )$

Explanation:

6x + 22 > 67

6x + 22 -22 > 67 -22

6x > 45

$6x \div 6 > 45\div 6$

x > 7.5

or, in interval notation, $\left ( 7.5, \infty \right )$

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 10 11 12 Next →

View Algebra 2 Tutors

Louis
Certified Tutor

University of California-Los Angeles, Bachelor in Arts, Film Production.

View Algebra 2 Tutors

Anthony
Certified Tutor

George Washington University, Bachelor of Science, Biology, General. Columbia University in the City of New York, Master of S...

View Algebra 2 Tutors

Kalpak
Certified Tutor

University of Toronto, Bachelor of Science, Chemical Engineering.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

English Tutors in Atlanta, Biology Tutors in New York City, Physics Tutors in Miami, Reading Tutors in Dallas Fort Worth, Physics Tutors in Denver, French Tutors in Dallas Fort Worth, Statistics Tutors in Seattle, ISEE Tutors in San Francisco-Bay Area, Physics Tutors in Chicago, GRE Tutors in San Francisco-Bay Area

Popular Courses & Classes

GMAT Courses & Classes in Seattle, SAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Atlanta, MCAT Courses & Classes in Chicago, SSAT Courses & Classes in Houston, ISEE Courses & Classes in Miami, SAT Courses & Classes in Miami, MCAT Courses & Classes in Phoenix, GMAT Courses & Classes in Atlanta, SSAT Courses & Classes in Denver

Popular Test Prep

MCAT Test Prep in New York City, SSAT Test Prep in Boston, SAT Test Prep in San Diego, ACT Test Prep in Houston, SAT Test Prep in Boston, SSAT Test Prep in Seattle, SSAT Test Prep in Dallas Fort Worth, MCAT Test Prep in San Francisco-Bay Area, GRE Test Prep in Atlanta, SSAT Test Prep in Chicago

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

Algebra II : Solving Inequalities

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Solving Inequalities

Example Question #1 : Solving Inequalities

Example Question #1 : Graphing Inequalities

Example Question #1 : Solving Inequalities

Example Question #1 : Solving Inequalities

Example Question #4 : Solving Inequalities

Example Question #5 : Solving Inequalities

Example Question #6 : Solving Inequalities

Example Question #7 : Solving Inequalities

Example Question #1 : Solving Inequalities

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: