Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Equations / Inequalities

圣udy concepts, example questions & explanations for Algebra 1

Create An Account Create Tests & Flashcards

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 … 33 34 Next →

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

Solve the inequality:

$\small \frac{5}{7}x > 15$

Possible Answers:

$\small x> \frac{100}{7}$

$\small x>21$

$\small x> \frac{110}{7}$

$\small x>\frac{25}{49}$

$\small x<-21$

Correct answer:

$\small x>21$

Explanation:

In order to isolate the variable, we need to remove the coefficient. Since the operation between $\tiny \small \frac{5}{7}$ and $\small x$ is multiplication, we may want to divide both sides of the inequality by $\tiny \small \frac{5}{7}$ . Although this is a valid step, in order to simplify matters, instead of dividing by $\tiny \small \frac{5}{7}$ , we can multiplying by $\small \frac{7}{5}$ .

(Note: dividing by $\frac{5}{7}$ 由reciproca multplying完全一样吗l, $\frac{7}{5}$ .)

Thus,

$\small x> \frac{15}{1} \cdot\frac{7}{5}$ and after multiplying and simplifying, we obtain $\small x>21$ .

Report an Error

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

Solve for:

3x-2-x>-2x+6

Possible Answers:

None of the other answers

x<2

x<-2

x>-2

x>2

Correct answer:

x>2

Explanation:

Simplify 3x-2-x>-2x+6 by combining like terms to get 2x-2>-2x+6 .

Then, addandto both sides to separate the's and intergers. This gives you 4x>8 .

Divide both sides to get x>2 . Since we didn't divide by a negative number, there is no need to reverse the sign.

Report an Error

Example Question #2 :How To Find The Solution To An Inequality With Multiplication

Solve for:

$\frac{7}{9} x > \frac{5}{3}$

Possible Answers:

$\left ( \frac{5}{3},\infty \right )$

$\left ( \frac{7}{3},\infty \right )$

$\left ( \frac{11}{7},\infty \right )$

$\left ( \frac{15}{7},\infty \right )$

$\left ( \frac{13}{7},\infty \right )$

Correct answer:

$\left ( \frac{15}{7},\infty \right )$

Explanation:

$\frac{7}{9} x > \frac{5}{3}$

$\frac{7}{9} x \div \frac{7}{9}> \frac{5}{3} \div \frac{7}{9}$

$\frac{7}{9} x \cdot \frac{9}{7}> \frac{5}{3}\cdot \frac{9}{7}$

Cross-cancel:

$x> \frac{5}{1}\cdot \frac{3}{7}$

$x> \frac{15}{7}$

or, in interval form, $\left ( \frac{15}{7},\infty \right )$ .

Report an Error

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

Solve for:

$\frac{2}{9} x + \frac{1}{3} < \frac{5}{6}$

Possible Answers:

The inequality has no solution.

$x < \frac{9}{4}$

$x < \frac{13}{4}$

$x < \frac{21}{4}$

$x < \frac{17}{4}$

Correct answer:

$x < \frac{9}{4}$

Explanation:

Eliminate fractions by multiplying by the least common denominator - LCM(3,6,9) = 18 .

$18 \cdot \left (\frac{2}{9} x + \frac{1}{3} \right ) <18 \cdot \frac{5}{6}$

$\frac{18}{1} \cdot \frac{2}{9} x + \frac{18}{1} \cdot \frac{1}{3} \right ) <\frac{18}{1} \cdot \frac{5}{6}$

Cross-cancel:

$\frac{2}{1} \cdot \frac{2}{1} x + \frac{6}{1} \cdot \frac{1}{1} \right ) <\frac{3}{1} \cdot \frac{5}{1}$

4x + 6 < 15

4x + 6 - 6 < 15 - 6

4x < 9

$4x \div 4 < 9 \div 4$

$x < \frac{9}{4}$

Report an Error

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

Find the solution set for:

$-\frac{7}{10} < -\frac{2}{5} x \leq \frac{1}{10}$

Possible Answers:

$\left ( - \frac{7}{4},\frac{1}{4} \right ]$

$\left ( - \frac{1}{4},\frac{7}{4} \right ]$

$\left [ \frac{1}{4},\frac{7}{4} \right )$

$\left [ -\frac{7}{4},-\frac{1}{4} \right )$

$\left [ - \frac{1}{4},\frac{7}{4} \right )$

Correct answer:

$\left [ - \frac{1}{4},\frac{7}{4} \right )$

Explanation:

$-\frac{7}{10} < -\frac{2}{5} x \leq \frac{1}{10}$

$- \frac{5}{2} \cdot \left (-\frac{7}{10} \right )> - \frac{5}{2} \cdot \left ( -\frac{2}{5}x \right ) \geq - \frac{5}{2} \cdot \frac{1}{10}$

Note the switch in inequality symbols when the numbers are multiplied by a negative number.

$\frac{5}{2} \cdot \frac{7}{10} > x \geq - \frac{5}{2} \cdot \frac{1}{10}$

Cross-cancel:

$\frac{1}{2} \cdot \frac{7}{2} > x \geq - \frac{1}{2} \cdot \frac{1}{2}$

$\frac{7}{4} > x \geq - \frac{1}{4}$

or, in interval form, $\left [ - \frac{1}{4},\frac{7}{4} \right )$

Report an Error

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

Solve for:

3x+4>9x-8

Possible Answers:

x>2

x>-2

None of the other answers are correct.

x<-2

x<2

Correct answer:

x<2

Explanation:

Subtract 4 from both sides. Then subtract 9x:

-6x>-12

Next divide both sides by -6. Don't forget to switch the inequality because of the negative sign!

x<2

Report an Error

Example Question #7 :How To Find The Solution To An Inequality With Multiplication

Solve for:

3x-12>x+2

Possible Answers:

None of the other answers are correct.

x<7

x<5

x>7

x>5

Correct answer:

x>7

Explanation:

To solve the inequality, subtractand add 12 to both sides to separate thefrom the integers:

2x>14

Divide both sides by 2:

x>7

Note: The inequality sign is only flipped when dividing by negative numbers.

Report an Error

Example Question #2 :How To Find The Solution To An Inequality With Multiplication

Solve for:

3x-5>5x+1+x

Possible Answers:

None of the other answers are correct.

x>4

x<-2

x>-2

x<4

Correct answer:

x<-2

Explanation:

首先,把右手的sid同类项e of the inequality to get 3x-5>6x+1 .

Then, subtractandfrom both sides to get -6>3x .

Finally, divide both sides by: x<-2

Report an Error

Example Question #1 :Equations / Inequalities

Solve this inequality.

-3x+2 < x+4

Possible Answers:

$x>-\frac{1}{2}$

x<1

$x<-\frac{1}{2}$

$x>\frac{1}{2}$

x>2

Correct answer:

$x>-\frac{1}{2}$

Explanation:

Isolate all the terms withon one side and the other terms on the other side and solve for.

-3x+2 < x+4

First subtract the an x from both sides of the inequality. The subtract 2 from each side. This results in the following inequality.

-4x<2

Here, we need to divide both sides by. However, whenever we divide or multiply and inequality by a negative number, we have to also change the direction of the inequality.

The final answer becomes

$x>-\frac{1}{2}$ .

Report an Error

Example Question #10 :How To Find The Solution To An Inequality With Multiplication

$2x\leq6$

Find all of the solutions to this inequality.

Possible Answers:

$(\infty, 6)$

$[6,\infty )$

$[\infty ,3]$

$(-\infty,3]$

$(3,\infty )$

Correct answer:

$(-\infty,3]$

Explanation:

To solve an inequality, isolate the variable on one side with all other constants on the other side. To accomplish this, perform opposite operations to manipulate the inequality.

First, isolate the x by multiplying each side by two.

Whatever you do to one side you must also do to the other side.

$\frac{2x}{{\color{Blue} 2}}\leq\frac{6}{{\color{Blue} 2}}$

This gives you:

$x\leq3$

The answer, therefore, is $(-\infty ,3]$ .

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 … 33 34 Next →

View Algebra Tutors

Michael
Certified Tutor

Cleveland State University, Bachelor of Science, Mathematics.

View Algebra Tutors

Hannah
Certified Tutor

University of Tulsa, Bachelor in Arts, Theater Arts.

View Algebra Tutors

Rosie
Certified Tutor

Texas State University-San Marcos, Bachelors, Mathematics. Texas State University-San Marcos, Masters, Mathematics.

All Algebra 1 Resources

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

Popular Subjects

Spanish Tutors in Boston,GRE Tutors in New York City,Chemistry Tutors in Seattle,LSAT Tutors in Boston,Chemistry Tutors in Los Angeles,MCAT Tutors in Los Angeles,GRE Tutors in Los Angeles,GMAT Tutors in New York City,Biology Tutors in San Francisco-Bay Area,ISEE Tutors in Washington DC

Popular Courses & Classes

Spanish Courses & Classes in Houston,GMAT Courses & Classes in Washington DC,Spanish Courses & Classes in Washington DC,GRE Courses & Classes in Seattle,SSAT Courses & Classes in Houston,GMAT Courses & Classes in Los Angeles,ACT Courses & Classes in San Francisco-Bay Area,GMAT Courses & Classes in Dallas Fort Worth,LSAT Courses & Classes in Dallas Fort Worth,MCAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

SAT Test Prep in Denver,GMAT Test Prep in Phoenix,ACT Test Prep in San Diego,MCAT Test Prep in San Francisco-Bay Area,ISEE Test Prep in Phoenix,SSAT Test Prep in Denver,SSAT Test Prep in Philadelphia,ACT Test Prep in Boston,MCAT Test Prep in Phoenix,MCAT 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:

copyrigh的物理或电子签名t 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
圣. 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

*圣ate

*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 : Equations / Inequalities

圣udy concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

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

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

Example Question #2 :How To Find The Solution To An Inequality With Multiplication

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

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

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

Example Question #7 :How To Find The Solution To An Inequality With Multiplication

Example Question #2 :How To Find The Solution To An Inequality With Multiplication

Example Question #1 :Equations / Inequalities

Example Question #10 :How To Find The Solution To An Inequality With Multiplication

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Find the Best Tutors

Email address:
Your name:
Feedback: