Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Algebra II

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

Example Question #3 : Solving Inequalities

Solve the inequality:

$\small x^2+4< 9$

Possible Answers:

$\small x< -\sqrt5$

$\small x< \sqrt5$

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

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

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 #3 : Solving Inequalities

Solve for :

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

Possible Answers:

$x \geq 3$

$x \geq -3$

x < -3

$x \leq 3$

$x \leq -3$

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 : Writing Inequalities

Find the solution set of the inequality:

6x + 22 > 67

Possible Answers:

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

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

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

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

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

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

Example Question #1 : Writing Inequalities

Solve for :

$3(x + 4) \leq x - 6$

Possible Answers:

$x \geq 9$

$x \leq 3$

$x \leq 9$

$x \geq -9$

$x \leq -9$

Correct answer:

$x \leq -9$

Explanation:

The first step is to distribute (multiply) through the parentheses:

$3(x + 4) \leq x - 6$

$3x + 12 \leq x - 6$

Then subtract from both sides of the inequality:

$2x + 12 \leq -6$

Next, subtract the 12:

$2x \leq -18$

Finally, divide by two:

$x \leq -9$

Report an Error

Example Question #3 : Graphing Inequalities

Axes_2

Which of the following inequalities is graphed above?

Possible Answers:

$y \geq \frac{7}{2} x + 7$

$y \geq \frac{7}{2} x -2$

$y \leq \frac{2}{7} x + 7$

$y \leq \frac{7}{2} x + 7$

$y \leq \frac{7}{2} x -2$

Correct answer:

$y \leq \frac{7}{2} x + 7$

Explanation:

First, we determine the equation of the boundary line. This line includes points (0, 7) and (-2,0) , so the slope can be calculated as follows:

$m = \frac{y_{2}- y_{1}}{x_{2}- x_{1}} = \frac{7-0}{0- (-2)} = \frac{7}{2}$

Since we also know the -intercept is (0,7) , we can substitute $m = \frac{7}{2}, b = 7$ in the slope-intercept form to obtain equation of the boundary:

y = mx+b

$y = \frac{7}{2} x + 7$

The boundary is included, as is indicated by the line being solid, so the equality symbol is replaced by either $\leq$ or $\geq$ . To find out which one, we can test a point in the solution set - for ease, we will choose (0,0) :

_____ $\frac{7}{2} x + 7$

_____ $\frac{7}{2} \cdot 0+ 7$

_____

0 is less than 7 so the correct symbol is $\leq$ .

The correct choice is $y \leq \frac{7}{2} x + 7$ .

Report an Error

Example Question #2081 : Algebra Ii

Solve for .

$\frac{x}{3}-2\geq13$

Possible Answers:

x>45

$x\geq15$

$x\geq45$

x>5

$x\geq5$

Correct answer:

$x\geq45$

Explanation:

First, add 2 to both sides of the inequality:

$\frac{x}{3}-2+2\geq13+2$ and simplify: $\frac{x}{3}\geq15$ .

Then, multiply each side by 3:

$3\cdot\frac{x}{3}\geq15\cdot3$ and simplify: $x\geq45$ .

Report an Error

Example Question #242 : Algebra Ii

Solve for :

$5-3x\leq14$

Possible Answers:

$x\geq0$

$x\geq3$

$x\geq9$

$x\leq3$

$x\geq-3$

Correct answer:

$x\geq-3$

Explanation:

Inequalities can be treated like any other equation except when multiplying and dividing by negative numbers. When multiplying or dividing by negative numbers, we just flip the sign of the inequality so that becomes , and vice versa.

$5-3x\leq14$

$-3x\leq9$

$\frac{-3x}{-3}\geq\frac{9}{-3}$

$x\geq-3$

Report an Error

Example Question #13 : Solving Inequalities

Find the solution set of the following inequality.

x^2+3x>-2

Possible Answers:

$(-1,\infty)$

$(-\infty,-1)\cup(1,\infty)$

$(-\infty,\infty)$

$(-\infty,-2)\cup(-1,\infty)$

$(-\infty,-2)$

Correct answer:

$(-\infty,-2)\cup(-1,\infty)$

Explanation:

To make this problem easier to solve, we can add 2 to both sides so that we can factor the left side of the expression.

x^2+3x+2>0

(x+2)(x+1)>0

The breakpoints to examine are at x=-2,-1

These two breakpoints create 3 total regions that we need to examine:

$(-\infty,-2)$ , (-2,-1) , and $(-1,\infty)$ . Which ever region satisfies the expression above will be a solution to the inequality.

A value of -3 gives us: (-3+2)(-3+1)=2 .

is greater than 0, so it satisfies the inequality.

A value of -1.5 for the second region does not satisfy the inequality.

A value of 0 for the third region does satify the inequality, so the first and third regions give us our answer.

$(-\infty,-2)\cup(-1,\infty)$ .

Report an Error

View Algebra 2 Tutors

Ataul
Certified Tutor

Temple University, Bachelor of Science, Financial Planning.

View Algebra 2 Tutors

Dr. Derrick
Certified Tutor

Huston-Tillotson University, Bachelor of Science, Mathematics. Grand Canyon University, Master of Arts, Education.

View Algebra 2 Tutors

Kavya
Certified Tutor

North Carolina State University, Master's/Graduate, Financial Mathematics.

All Algebra II Resources

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

Popular Subjects

French Tutors in Houston, Chemistry Tutors in Philadelphia, Computer Science Tutors in Atlanta, Spanish Tutors in Miami, ACT Tutors in Boston, SAT Tutors in Dallas Fort Worth, Statistics Tutors in San Diego, SAT Tutors in San Diego, MCAT Tutors in Phoenix, Reading Tutors in Los Angeles

Popular Courses & Classes

ISEE Courses & Classes in Boston, LSAT Courses & Classes in Chicago, ACT Courses & Classes in Denver, ISEE Courses & Classes in Houston, SAT Courses & Classes in San Diego, MCAT Courses & Classes in Houston, GRE Courses & Classes in San Diego, LSAT Courses & Classes in San Diego, SAT Courses & Classes in Houston, ACT Courses & Classes in New York City

Popular Test Prep

SSAT Test Prep in Los Angeles, SSAT Test Prep in Denver, ISEE Test Prep in San Diego, GRE Test Prep in San Diego, SSAT Test Prep in Seattle, SAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Dallas Fort Worth, ACT Test Prep in Denver, GMAT Test Prep in Denver, LSAT Test Prep in Washington DC

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 : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #3 : Solving Inequalities

Example Question #5 : Solving Inequalities

Example Question #3 : Solving Inequalities

Example Question #7 : Solving Inequalities

Example Question #1 : Writing Inequalities

Example Question #1 : Writing Inequalities

Example Question #3 : Graphing Inequalities

Example Question #2081 : Algebra Ii

Example Question #242 : Algebra Ii

Example Question #13 : Solving Inequalities

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: