We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Systems of Inequalities

Study concepts, example questions & explanations for Algebra 1

Create An Account

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 7 8 9 … 12 13 Next →

Example Question #2142 : Algebra 1

Solve: $\frac{4}{7}x > 7$

Possible Answers:

$x>\frac{1}{4}$

$x<\frac{45}{4}$

x>4

$x<\frac{49}{4}$

$x>\frac{49}{4}$

Correct answer:

$x>\frac{49}{4}$

Explanation:

To isolate the x variable, multiply the reciprocal of the fraction in front of the variable on both sides of the inequality.

$\frac{4}{7}x \cdot \frac{7}{4}> 7\cdot \frac{7}{4}$

Simplify both sides of the inequality.

The answer is: $x>\frac{49}{4}$

Report an Error

Example Question #21 : Systems Of Inequalities

Solve the following inequality: $\frac{1}{3}x + \frac{2}{3}>3$

Possible Answers:

x<7

$x>-\frac{7}{3}$

x>1

x>7

$x>\frac{7}{3}$

Correct answer:

x>7

Explanation:

In order to eliminate the fractions, multiply the inequality by three on both sides.

This will make the inequality easier to solve.

$3(\frac{1}{3}x + \frac{2}{3})>3(3)$

Distribute and simplify both sides.

x+2>9

Subtract two from both sides.

x+2-2>9-2

The answer is: x>7

Report an Error

Example Question #23 : Equations / Inequalities

Solve the inequality: $\frac{2}{3}x >15$

Possible Answers:

$x>\frac{43}{3}$

$x<\frac{43}{3}$

$x>\frac{13}{3}$

$x<\frac{45}{2}$

$x>\frac{45}{2}$

Correct answer:

$x>\frac{45}{2}$

Explanation:

Multiply both sides by three halves.

$\frac{2}{3}x \cdot \frac{3}{2} >15 \cdot \frac{3}{2}$

Simplify both sides. Multiply the integer with the numerator on the right side of the inequality.

The answer is: $x>\frac{45}{2}$

Report an Error

Example Question #21 : Systems Of Inequalities

Solve the following inequality: $\frac{2}{7}x <7$

Possible Answers:

$x<\frac{49}{2}$

$x>\frac{49}{2}$

$x<\frac{47}{7}$

$x\leq\frac{49}{2}$

$x\leq\frac{47}{7}$

Correct answer:

$x<\frac{49}{2}$

Explanation:

Solve this inequality by multiplying both sides by the reciprocal of the coefficient in front of the x-variable.

$\frac{2}{7}x \cdot \frac{7}{2} <7\cdot \frac{7}{2}$

Simplify both sides. Multiply the integer by the numerator on the right side of the inequality.

The answer is: $x<\frac{49}{2}$

Report an Error

Example Question #25 : Equations / Inequalities

Solve the following inequality: $\frac{2}{5}x>40$

Possible Answers:

$x>\frac{35}{2}$

x>10

x>100

x>4

x>16

Correct answer:

x>100

Explanation:

Multiply the reciprocal of the fraction in front of the variable on both sides of the equation.

$\frac{2}{5}x \cdot \frac{5}{2}>40\cdot \frac{5}{2}$

Simplify both sides.

$x>\frac{200}{2}$

Reduce the fraction on the right side.

The answer is: x>100

Report an Error

Example Question #26 : Equations / Inequalities

Solve the inequality: $\frac{3}{4}x>-4$

Possible Answers:

$x>-\frac{1}{3}$

$x<-\frac{16}{3}$

$x>-\frac{16}{3}$

x>-2

x>-4

Correct answer:

$x>-\frac{16}{3}$

Explanation:

Multiply both sides by the reciprocal of the fraction in front of the x-variable.

$\frac{3}{4}x\cdot \frac{4}{3}>-4\cdot \frac{4}{3}$

Simplify both sides. There is no need to switch the sign. Multiply the negative integer with the numerator on the right side of the inequality.

The answer is: $x>-\frac{16}{3}$

Report an Error

Example Question #27 : Equations / Inequalities

Solve the inequality: $9x\leq -\frac{1}{3}$

Possible Answers:

$x\leq -\frac{1}{3}$

$x\geq -\frac{1}{3}$

$x\geq -\frac{1}{27}$

$x\leq -\frac{1}{27}$

$x< -\frac{1}{27}$

Correct answer:

$x\leq -\frac{1}{27}$

Explanation:

In order to isolate the x-variable, we will need to divide both sides by nine. To avoid writing a complex fraction on the right side, dividing by nine is similar to multiplying by one-ninth.

Multiply by one-ninth on both sides.

$9x \cdot \frac{1}{9}\leq -\frac{1}{3} \cdot \frac{1}{9}$

Simplify both sides. Multiply the denominator with denominator on the right side. Since we have divide by a positive number on both sides, there is no need to switch the sign.

The answer is: $x\leq -\frac{1}{27}$

Report an Error

Example Question #1 : How To Find The Solution To An Inequality With Subtraction

Solve the inequality:

$\small x+12>4+3$

Possible Answers:

$\small x>-5$

$\small x>19$

$\small x<-19$

$\small x>11$

$\small x<5$

Correct answer:

$\small x>-5$

Explanation:

First combine like terms on the right side of the inequality to obtain $\small x+12>7$ . Next, try to isolate the variable: $\small x+12\mathbf{-12} >7\mathbf{-12}$ .

The answer is therefore $\small x>-5$ .

Report an Error

Example Question #1 : How To Find The Solution To An Inequality With Subtraction

Solve the inequality:

$\small -(-x-4)\le6$

Possible Answers:

$\small x\le2$

$\small x \ge2$

$\small x\ge-2$

$\small x\le-10$

$\small x\le-2$

Correct answer:

$\small x\le2$

Explanation:

Distribute the negative sign first: $\small -(-x-4)\le6$ becomes $\small x+4\le6$ . Since there are no like-terms to combine on one side of the inequality sign, we will try to isolate the variable: $\small x+4\boldsymbol{-4} \le 6\boldsymbol{-4}$ . The answer is therefore $\small x\le2$ .

Report an Error

Example Question #3 : How To Find The Solution To An Inequality With Subtraction

$\left | 4x+4 \right |< 20$

Which one of the following is is a valid value for ?

Possible Answers:

Correct answer:

Explanation:

Since the inequality includes absolute value, you have two possiblities to consider: when the outcome is positive and when it is negative. When you consider the negative outcome, you must flip the inequality sign to solve for :

|4x+4|<20

This means that 4x+4 is less than positive 20 AND greater than negative 20:

4x+4<20 AND 4x+4 > -20

For each case, you will first subtract 4 from the left to the right. Then, you will divide both sides by 4 to isolate :

4x<16 AND 4x>-24

x<4 AND x>-6

This gives you the interval for valid values of :

-6<x<4

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 … 12 13 Next →

View Algebra Tutors

Vince
Certified Tutor

Salt Lake Community College, Associate in Science, Mathematics.

View Algebra Tutors

Dossevi
Certified Tutor

cole Ste Genevive Versailles, Bachelor of Science, Mathematics. Institut National Polytechnique de Grenoble, Master of Scienc...

View Algebra Tutors

Zhi Xuan
Certified Tutor

Queen's University, Bachelor, Engineering .

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Math Tutors in San Francisco-Bay Area, Physics Tutors in Miami, SSAT Tutors in Chicago, English Tutors in Atlanta, GRE Tutors in Seattle, Biology Tutors in New York City, Computer Science Tutors in Chicago, GMAT Tutors in Denver, LSAT Tutors in San Francisco-Bay Area, GMAT Tutors in Philadelphia

Popular Courses & Classes

ACT Courses & Classes in Miami, GMAT Courses & Classes in Boston, ACT Courses & Classes in New York City, GRE Courses & Classes in Miami, SAT Courses & Classes in Denver, MCAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Denver, SAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Houston, LSAT Courses & Classes in Phoenix

Popular Test Prep

ISEE Test Prep in Houston, ISEE Test Prep in Washington DC, MCAT Test Prep in Phoenix, GMAT Test Prep in Denver, GMAT Test Prep in Boston, ACT Test Prep in Phoenix, GMAT Test Prep in Miami, ISEE Test Prep in Atlanta, GRE Test Prep in New York City, MCAT Test Prep in Los Angeles

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 1 : Systems of Inequalities

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #2142 : Algebra 1

Example Question #21 : Systems Of Inequalities

Example Question #23 : Equations / Inequalities

Example Question #21 : Systems Of Inequalities

Example Question #25 : Equations / Inequalities

Example Question #26 : Equations / Inequalities

Example Question #27 : Equations / Inequalities

Example Question #1 : How To Find The Solution To An Inequality With Subtraction

Example Question #1 : How To Find The Solution To An Inequality With Subtraction

Example Question #3 : How To Find The Solution To An Inequality With Subtraction

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: