We are open Saturday and Sunday!

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 #1 : Absolute Value

Solve for :

$\left |2x+3 \right |>7$

Possible Answers:

x<2, x>-5

x>2

x>2, x<-5

x>3.5, x<-5

x>2, x<-10

Correct answer:

x>2, x<-5

Explanation:

Solve for positive values by ignoring the absolute value. Solve for negative values by switching the inequality and adding a negative sign to 7.

Report an Error

Example Question #4791 : Algebra Ii

Give the solution set for the following equation:

| 4x - 7 | + 5 = 86

Possible Answers:

$\begin{Bmatrix} -18.5, 22 \end{Bmatrix}$

$\begin{Bmatrix} 18.5, 22 \end{Bmatrix}$

$\begin{Bmatrix} 22 \end{Bmatrix}$

$\begin{Bmatrix} -24.5, 22 \end{Bmatrix}$

$\begin{Bmatrix} 22, 24.5 \end{Bmatrix}$

Correct answer:

$\begin{Bmatrix} -18.5, 22 \end{Bmatrix}$

Explanation:

First, subtract 5 from both sides to get the absolute value expression alone.

| 4x - 7 | + 5 = 86

| 4x - 7 | = 81

Split this into two linear equations:

4x - 7 = 81

4x = 88

x = 22

4x - 7 = -81

4x = -74

$x = -74 \div 4 = -18.5$

The solution set is $\begin{Bmatrix} -18.5, 22 \end{Bmatrix}$

Report an Error

Example Question #2 : Absolute Value

Solve for in the inequality below.

$|x-2| \leq 4$

Possible Answers:

$x\leq -2\; \; or\; \; x\geq 6$

No solutions

$x\leq 4$

$-2 \leq x\leq 6$

All real numbers

Correct answer:

$-2 \leq x\leq 6$

Explanation:

The absolute value gives two problems to solve. Remember to switch the "less than" to "greater than" when comparing the negative term.

$x-2\leq 4$ or $x-2\geq -4$

Solve each inequality separately by adding to all sides.

$x\leq 6$ or $x\geq -2$

This can be simplified to the format $-2 \leq x\leq 6$ .

Report an Error

Example Question #1 : Absolute Value Inequalities

$\textup{If }\left | 2x+4\right |\leq10\textup{ , what are all possible values of }x\textup{?}$

Possible Answers:

$-7\leq x\leq3$

$-3\leq x\leq7$

$x\leq-7\textup{ and }x\geq3$

x=-7,x=3

$-3\leq x\leq3$

Correct answer:

$-7\leq x\leq3$

Explanation:

$\textup{Set up two inequalities. Reverse the inequality sign for the negative one.}$

$2x+4\leq10\;\;\;\;\;\;\;\;\;\;\;\;\;2x+4\geq-10$

$2x\leq6\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \; 2x\geq-14$

$x\leq3\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x\geq-7$

Report an Error

Example Question #11 : Solving Absolute Value Equations

Solve the inequality.

$\small \left | x+2 \right |>5$

Possible Answers:

$\small -3<x<7$

$\small x<-3\ or\ x>7$

$\small -7<x<3$

$\small x<-7\ or\ x>3$

Correct answer:

$\small x<-7\ or\ x>3$

Explanation:

$\small \left | x+2 \right |>5$

Remove the absolute value by setting the term equal to either $\small 5$ or $\small -5$ . Remember to flip the inequality for the negative term!

$\small x+2>5\ or\ x+2<-5$

Solve each scenario independently by subtracting $\small 2$ from both sides.

$\small x+2-2>5-2\ or\ x+2-2<-5-2$

$\small x>3\ or\ x<-7$

Report an Error

Example Question #12 : Solving Absolute Value Equations

Solve for :

| 4y + 7 | > -5

Possible Answers:

$(-\infty , -3) \cup \left ( \frac{1}{2}, \infty \right)$

$(-\infty , \infty )$

$\left(-\infty , -\frac{1}{2}\right) \cup \left (3, \infty \right)$

$(-\infty , -3) \cup (3, \infty )$

$\left(-\infty , -\frac{1}{2}\right) \cup \left ( \frac{1}{2}, \infty \right)$

Correct answer:

$(-\infty , \infty )$

Explanation:

The absolute value of any number is nonnegative, so | 4y + 7 | must always be greater than . Therefore, any value of makes this a true statement.

Report an Error

Example Question #11 : Absolute Value Inequalities

Solve the following inequality.

$\left | x-6\right |+8>12$

Possible Answers:

$x>-10\:or\:x<2$

$x>10\:or\:x<-14$

2<x<10

x>2

$x>10\:or\:x<2$

Correct answer:

$x>10\:or\:x<2$

Explanation:

Inequalities involving $> \: or\: \geq$ generate two separate inequalities and can't be combined into a single inequality.

First isolate the absolute value expression on one side of the inequality

$\left | x-6\right |+8>12$

Subtract eight from each side.

$\left |x-6 \right |>4$

From here separate the expression into two expressions for which we will need to solve.

$x-6>4\: \: \: \:or\: \: \: \:x-6<-4$

Add six to get side.

$x>10\: \: \: \:or\: \: \: \:x<2$

Report an Error

Example Question #11 : Absolute Value Inequalities

Solve the inequality for .

$\left | 3x+5\right |\geq 1$

Possible Answers:

$x\geq -2$

$x\leq -2$ and $x\geq -\frac{4}{3}$

$-2\leq x\leq -\frac{4}{3}$

$x\geq -\frac{4}{3}$

$x\geq -\frac{4}{3}$ and $x\leq \frac{4}{3}$

Correct answer:

$x\leq -2$ and $x\geq -\frac{4}{3}$

Explanation:

To solve an inequality with absolute value you have to consider the two equations it creates.

$\left | 3x+5\right |\geq 1$ becomes $3x+5\geq 1$ and $3x+5\leq -1$

Solve for both inequalities by following the balancing rules. Be careful of division or multiplication of a negative number; if that happens, flip the inequality sign.

$3x+5\geq 1$

$3x\geq -4$

$x\geq -\frac{4}{3}$

$3x+5\leq -1$

$3x\leq -6$

$x\leq -2$

Report an Error

Example Question #12 : Absolute Value Inequalities

$\left | 3x\right |<27$

Possible Answers:

x>9

-9<x<9

x<-9,x>9

x<-8,x>8

-30<x<30

Correct answer:

-9<x<9

Explanation:

We first need to eliminate the absolute value sign by making two inequalities:

3x<27 and 3x>-27 . Remember that when the number becomes negative we must flip the inequality symbol.

From there, it is a simple one-step inequality. We divide both sides by to get:

x<9

x>-9 .

Because x lies between and , we can combine these into one inequality:

-9<x<9

Report an Error

Example Question #13 : Absolute Value Inequalities

Solve the inequality: $\left | 2x+3\right |>4$

Possible Answers:

$[\frac{1}{2}, \infty)$

$(-\infty. -\frac{7}{2})\bigcup (\frac{1}{2}, \infty)$

$(-\infty. -\frac{1}{2})\bigcup (\frac{7}{2}, \infty)$

$(-\frac{7}{2}, \infty)$

$(-\infty. -\frac{7}{2}]\bigcup [\frac{1}{2}, \infty)$

Correct answer:

$(-\infty. -\frac{7}{2})\bigcup (\frac{1}{2}, \infty)$

Explanation:

Split up the absolute value and rewrite the inequalities in two formats:

2x+3>4

-(2x+3)>4

Solve the first inequality. Subtract three on both sides.

2x>1

Divide by two on both sides.

The first solution is: $x> \frac{1}{2}$

Evaluate the second inequality.

Divide negative one on both sides. Dividing a negative term will switch the sign.

2x+3<-4

Subtract three on both sides.

2x<-7

Divide by two on both sides.

The second solution is: $x<-\frac{7}{2}$

In interval notation, the answer is: $(-\infty. -\frac{7}{2})\bigcup (\frac{1}{2}, \infty)$

Report an Error

View Algebra Tutors

Jack
Certified Tutor

University of Washington-Seattle Campus, Bachelor in Arts, Mathematics. Western Washington University, Master of Science, Mat...

View Algebra Tutors

Celestine
Certified Tutor

University of Ghana, Bachelor of Science, Agricultural Economics. University of Minnesota-Twin Cities, Doctor of Philosophy, ...

View Algebra Tutors

Soung
Certified Tutor

University of Chicago, Bachelor in Arts, Chemistry. Northwestern University, Doctor of Science, Molecular Pharmacology.

All Algebra 1 Resources

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

Popular Subjects

Chemistry Tutors in Miami, English Tutors in Boston, SAT Tutors in Chicago, Spanish Tutors in San Francisco-Bay Area, GMAT Tutors in Atlanta, ACT Tutors in Atlanta, GRE Tutors in Seattle, GMAT Tutors in Miami, Physics Tutors in Philadelphia, English Tutors in Washington DC

Popular Courses & Classes

ACT Courses & Classes in Philadelphia, SAT Courses & Classes in Atlanta, LSAT Courses & Classes in Chicago, MCAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Seattle, ISEE Courses & Classes in Miami, SSAT Courses & Classes in Washington DC, MCAT Courses & Classes in Houston, ACT Courses & Classes in Dallas Fort Worth

Popular Test Prep

GRE Test Prep in Phoenix, GMAT Test Prep in Philadelphia, ISEE Test Prep in Phoenix, ISEE Test Prep in Chicago, ISEE Test Prep in Washington DC, ACT Test Prep in San Diego, SAT Test Prep in Houston, ACT Test Prep in Philadelphia, LSAT Test Prep in Los Angeles, SSAT Test Prep in Philadelphia

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 #1 : Absolute Value

Example Question #4791 : Algebra Ii

Example Question #2 : Absolute Value

Example Question #1 : Absolute Value Inequalities

Example Question #11 : Solving Absolute Value Equations

Example Question #12 : Solving Absolute Value Equations

Example Question #11 : Absolute Value Inequalities

Example Question #11 : Absolute Value Inequalities

Example Question #12 : Absolute Value Inequalities

Example Question #13 : Absolute Value Inequalities

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: