Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Algebra 1

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

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

Give the solution set of the inequality:

-4x + 11 < 67

Possible Answers:

$(-\infty ,-14 )$

The set of all real numbers

$(-\infty ,14 )$

$(-14, \infty )$

(-14,14)

Correct answer:

$(-14, \infty )$

Explanation:

-4x + 11 < 67

-4x + 11 - 11 < 67- 11

-4x < 56

$-4x \div (-4) > 56 \div (-4)$

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

x > -14

or, in interval form,

$(-14, \infty )$

Report an Error

Example Question #91 : Equations / Inequalities

Solve for :

2-6x>10-2x

Possible Answers:

x>-2

None of the other answers

x<2

x<-2

x>2

Correct answer:

x<-2

Explanation:

First, add and subtract from both sides of the inequality to get -4x>8 .

Then, divide both sides by and reverse the sign since you are dividing by a negative number.

This gives you x<-2 .

Report an Error

Example Question #2221 : Algebra 1

Find the solution set to the following compound inequality statement:

$4y + 15 < 91 \textrm{ and } 7y -12 > 86$

Possible Answers:

(14,19)

$(-\infty , 19)$

$(14, \infty )$

$(-\infty , \infty )$

$(-\infty , 14) \cup (19, \infty )$

Correct answer:

(14,19)

Explanation:

Solve each of these two inequalities separately:

4y + 15 < 91

4y + 15 - 15 < 91- 15

4y < 76

$4y \div 4 < 76 \div 4$

y < 19 , or, in interval form, $(-\infty , 19)$

7y -12 > 86

7y -12 + 12 > 86 + 12

7y > 98

$7y \div 7 > 98 \div 7$

y > 14 , or, in interval form, $(14, \infty )$

The two inequalities are connected with an "and", so we take the intersection of the two intervals.

$(14, \infty ) \cap (-\infty , 19) = (14,19)$

Report an Error

Example Question #9 : How To Find The Solution To An Inequality With Division

Solve for :

$0.4 x - 1.7 \geq -8.5$

Possible Answers:

$[-17, \infty )$

$[1.7, \infty )$

The inequality has no solution.

$[-1.7, \infty )$

$[17, \infty )$

Correct answer:

$[-17, \infty )$

Explanation:

$0.4 x - 1.7 \geq -8.5$

$0.4 x - 1.7 + 1.7 \geq -8.5+ 1.7$

$0.4 x \geq -6.8$

$0.4 x \div 0.4 \geq -6.8\div 0.4$

$x \geq -17$

or, in interval form, $[-17, \infty )$

Report an Error

Example Question #93 : Equations / Inequalities

Find the solution set of the compound inequality:

$0.3x + 5 > 17 \textrm{ or } 0.7x - 3.1 < 1.6$

Possible Answers:

$(40,\infty )$

(7,40 )

$(-\infty ,40 )$

$(7,\infty )$

$(-\infty ,7) \cup (40,\infty )$

Correct answer:

$(-\infty ,7) \cup (40,\infty )$

Explanation:

Solve each inequality separately:

0.3x + 5 > 17

0.3x + 5 - 5 > 17- 5

0.3x > 12

$0.3x \div 0.3 > 12 \div 0.3$

x > 40

or, in interval form, $(40,\infty )$

0.7x - 3.1 < 1.6

0.7x - 3.1 + 3.1 < 1.6+ 3.1

0.7x < 4.9

$0.7x \div 0.7 < 4.9 \div 0.7$

x < 7

or, in interval form, $(-\infty ,7)$

Since these statements are connected by an "or", we are looking for the union of the intervals. Since the intervals are disjoint, we can simply write this as $(-\infty ,7) \cup (40,\infty )$

Report an Error

Example Question #94 : Equations / Inequalities

Find the solution set for :

$5.3 \geq -5x > -8.4$

Possible Answers:

[-1.68, -1.06)

[-1.06, 1.68)

(-1.06, 1.68]

[-1.68, 1.06)

(-1.68, 1.06]

Correct answer:

[-1.06, 1.68)

Explanation:

$5.3 \geq -5x > -8.4$

$5.3 \div (-5 ) \leq -5x \div (-5 ) < -8.4 \div (-5 )$

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

$-1.06 \leq x < 1.68$

or, in interval form:

[-1.06, 1.68)

Report an Error

Example Question #13 : How To Find The Solution To An Inequality With Division

Solve for :

7x-2>2x+8

Possible Answers:

x<4

x>2

x<2

x<3

x>3

Correct answer:

x>2

Explanation:

To solve the inequality, you must first separate the integers and the 's. Subtract and add to both sides of the inequality to get

5x>10 .

Then, divide both sides by to get

x>10 .

Since you are not dividing by a negative number, the sign does not need to be reversed.

Report an Error

Example Question #2222 : Algebra 1

Solve for :

6x-2>4(x+1)

Possible Answers:

x>3

x<3

x>2

None of the other answers

x>3

Correct answer:

x>3

Explanation:

First, use the distributive property to simplify the right side of the inequality:

6x-2>4x+4 .

Then, add and subtract from both sides of the inequality to get

2x>6 .

Finally, divide from both sides to get x>3 .

Report an Error

Example Question #2221 : Algebra 1

Find the solution set for the inequality.

-2x + 100 < 234

Possible Answers:

$\mathbb{R}$

$\left \{ x | x < - 67\; or\; x>67\right \}$

$\left \{ x | x < - 67\right \}$

$\left \{ x \left | x > -67\right \}$

Does not exist.

Correct answer:

$\left \{ x \left | x > -67\right \}$

Explanation:

-2x + 100 < 234

Subtract 100 from each side:

-2x + 100 - 100 < 234 - 100

-2x < 134

Divide both sides by -2:

x > - 67

(Note that the inequality symbol switched when we divided by a negative number.)

Report an Error

Example Question #2222 : Algebra 1

Solve for :

3x-1< x+5

Possible Answers:

x<3

None of the other answers are correct.

x>3

x<1

x>1

Correct answer:

x<3

Explanation:

To solve this inequality, get the 's to one side of the equation and the integers to the other side.

Add 1 to both sides:

2x<6

Divide both sides by 2:

x<3

(Since we are not dividing by a negative number, there is no need to reverse the sign.)

Report an Error

View Algebra Tutors

Tracy
Certified Tutor

Clarion University of Pennsylvania, Bachelor of Science, Physics.

View Algebra Tutors

Bobby
Certified Tutor

University of Houston - Downtown, Bachelor of Science, Applied Mathematics.

View Algebra Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

All Algebra 1 Resources

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

Popular Subjects

GMAT Tutors in Houston, Math Tutors in Philadelphia, LSAT Tutors in New York City, Physics Tutors in Denver, Reading Tutors in Philadelphia, SAT Tutors in Philadelphia, LSAT Tutors in Los Angeles, Algebra Tutors in New York City, Math Tutors in Houston, SAT Tutors in Houston

Popular Courses & Classes

ACT Courses & Classes in Houston, GRE Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in San Diego, ACT Courses & Classes in Chicago, SSAT Courses & Classes in Chicago, SSAT Courses & Classes in Phoenix, GRE Courses & Classes in Houston, SAT Courses & Classes in Chicago, ACT Courses & Classes in New York City, LSAT Courses & Classes in Denver

Popular Test Prep

GMAT Test Prep in Atlanta, SSAT Test Prep in Boston, LSAT Test Prep in Boston, ACT Test Prep in Houston, GRE Test Prep in Miami, ISEE Test Prep in Denver, LSAT Test Prep in Phoenix, GRE Test Prep in Dallas Fort Worth, GRE Test Prep in Houston, GRE Test Prep in Phoenix

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 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

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

Example Question #91 : Equations / Inequalities

Example Question #2221 : Algebra 1

Example Question #9 : How To Find The Solution To An Inequality With Division

Example Question #93 : Equations / Inequalities

Example Question #94 : Equations / Inequalities

Example Question #13 : How To Find The Solution To An Inequality With Division

Example Question #2222 : Algebra 1

Example Question #2221 : Algebra 1

Example Question #2222 : Algebra 1

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: