We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : How to find the solution to an inequality with addition

Study concepts, example questions & explanations for SAT Math

Create An Account

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

What values of x make the following statement true?

|x – 3| < 9

Possible Answers:

6 < x < 12

–12 < x < 6

x < 12

–6 < x < 12

–3 < x < 9

Correct answer:

–6 < x < 12

Explanation:

Solve the inequality by adding 3 to both sides to get x < 12. Since it is absolute value, x – 3 > –9 must also be solved by adding 3 to both sides so: x > –6 so combined.

Report an Error

Example Question #4 : How To Find The Solution To An Inequality With Addition

If –1 < w < 1, all of the following must also be greater than –1 and less than 1 EXCEPT for which choice?

Possible Answers:

w²

|w|

|w|^0.5

w/2

3w/2

Correct answer:

3w/2

Explanation:

3w/2 will become greater than 1 as soon as w is greater than two thirds. It will likewise become less than –1 as soon as w is less than negative two thirds. All the other options always return values between –1 and 1.

Report an Error

Example Question #5 : How To Find The Solution To An Inequality With Addition

Solve for .

$\left | z-3 \right |\geq 5$

Possible Answers:

$z\leq -3\ \text{or}\ z\geq 5$

$z\leq -2\ \text{or}\ z\geq 8$

$-2\leq z\leq 8$

$z\geq 8$

$-3\leq z\leq 5$

Correct answer:

$z\leq -2\ \text{or}\ z\geq 8$

Explanation:

Absolute value problems always have two sides: one positive and one negative.

First, take the problem as is and drop the absolute value signs for the positive side: z – 3 ≥ 5. When the original inequality is multiplied by –1 we get z – 3 ≤ –5.

Solve each inequality separately to get z ≤ –2 or z ≥ 8 (the inequality sign flips when multiplying or dividing by a negative number).

We can verify the solution by substituting in 0 for z to see if we get a true or false statement. Since –3 ≥ 5 is always false we know we want the two outside inequalities, rather than their intersection.

Report an Error

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

What values of make the statement $\left |5x-9 \right |\geq6$ true?

Possible Answers:

$x\geq5,x\leq \frac{1}{5}$

$x\geq4,x\leq -\frac{1}{2}$

$x\geq3, x\leq \frac{3}{5}$

$x\geq6,x\leq \frac{1}{3}$

$x\geq15,x\leq \frac{2}{5}$

Correct answer:

$x\geq3, x\leq \frac{3}{5}$

Explanation:

First, solve the inequality $5x-9 \geq6$ :

$5x-9 \geq6$

$5x\geq15$

$x\geq3$

Since we are dealing with absolute value, $5x-9\leq-6$ must also be true; therefore:

$5x-9\leq-6$

$5x\leq3$

$x\leq \frac{3}{5}$

Report an Error

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

Solve: $3x+2\le 49$

Possible Answers:

$x\le \frac{17}{3}$

$x\le \frac{47}{3}$

$x\ge \frac{47}{3}$

$x\le 17$

$x\le 47$

Correct answer:

$x\le \frac{47}{3}$

Explanation:

To solve $3x+2\le 49$ , isolate .

$3x\le 47$

Divide by three on both sides.

$x\le \frac{47}{3}$

Report an Error

Example Question #21 : Inequalities

Solve for .

-5x+17>62

Possible Answers:

x>-9

x=-9

$x\leq-9$

$x\geq-9$

x<-9

Correct answer:

x<-9

Explanation:

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.

-5x+17>62 Subtract on both sides.

-5x>45 Divide on both sides. Remember to flip the sign.

x<-9

Report an Error

Example Question #5 : How To Find The Solution To An Inequality With Addition

Solve for .

4x+7<5x+13

Possible Answers:

x>-6

$x\geq-6$

x=-6

$x\leq-6$

x<-6

Correct answer:

x>-6

Explanation:

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.

4x+7<5x+13 Subtract 4x,13 on both sides.

x<-6

Report an Error

Example Question #6 : How To Find The Solution To An Inequality With Addition

Solve for .

$\left | x+5\right |<8$

Possible Answers:

x=3, x=-13

x>3, x<-13

x>3

-13<x<3

x<-13

Correct answer:

-13<x<3

Explanation:

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.

$\left | x+5\right |<8$ We need to set-up two equations since its absolute value.

x+5<8 Subtract on both sides. x<3

-(x+5)<8 Divide on both sides which flips the sign.

x+5>-8 Subtract on both sides. x>-13

Since we have the 's being either greater than or less than the values, we can combine them to get -13<x<3 .

Report an Error

Example Question #23 : Inequalities

Solve for .

$\left | x+7\right |\leq3x+13$

Possible Answers:

$-3\leq x$

$3\leq x\leq 5$

$x\leq -3, x\leq -5$

$-5\leq x\leq -3$

$-5\leq x$

Correct answer:

$-3\leq x$

Explanation:

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.

$\left | x+7\right |\leq3x+13$ We need to set-up two equations since it's absolute value.

$x+7\leq 3x+13$ Subtract x, 7 on both sides.

$-6\leq 2x$ Divide on both sides.

$-3\leq x$

$-(x+7)\leq 3x+13$ Distribute the negative sign to each term in the parenthesis.

$-x-7\leq3x+13$ Add and subtract on both sides.

$-20\leq4x$ Divide on both sides.

$-5\leq x$ We must check each answer. Let's try .

$\left | 0+7\right |<3(0)+13$ 7<13 This is true therefore $-3\leq x$ is a correct answer. Let's next try .

$\left | -4+7\right |<3(-4)+13$ 3<1 This is not true therefore $-5\leq x$ is not correct.

Final answer is just $-3\leq x$ .

Report an Error

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

If $x+1< 4$ and $y-2<-1$ , then which of the following could be the value of x+y ?

Possible Answers:

Correct answer:

Explanation:

To solve this problem, add the two equations together:

$x+1<4$

$y-2<-1$

$x+1+y-2<4-1$

$x+y-1<3$

$x+y<4$

The only answer choice that satisfies this equation is 0, because 0 is less than 4.

Report an Error

View SAT Mathematics Tutors

Noah
Certified Tutor

Bard College, Bachelors, Philosophy and Creative Writing (Dual Major). Sarah Lawrence College, Master of Fine Arts, Creative ...

View SAT Mathematics Tutors

Priyanka
Certified Tutor

CUNY Hunter College, Bachelor in Arts, Economics.

View SAT Mathematics Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

SAT Math Tutors in Top Cities:

Atlanta SAT Math Tutors, Austin SAT Math Tutors, Boston SAT Math Tutors, Chicago SAT Math Tutors, Dallas Fort Worth SAT Math Tutors, Denver SAT Math Tutors, Houston SAT Math Tutors, Kansas City SAT Math Tutors, Los Angeles SAT Math Tutors, Miami SAT Math Tutors, New York City SAT Math Tutors, Philadelphia SAT Math Tutors, Phoenix SAT Math Tutors, San Diego SAT Math Tutors, San Francisco-Bay Area SAT Math Tutors, Seattle SAT Math Tutors, St. Louis SAT Math Tutors, Tucson SAT Math Tutors, Washington DC SAT Math Tutors

Popular Courses & Classes

ACT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Seattle, GMAT Courses & Classes in Miami, GRE Courses & Classes in Philadelphia, SAT Courses & Classes in Boston, Spanish Courses & Classes in San Diego, SAT Courses & Classes in Atlanta, Spanish Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Boston, SAT Courses & Classes in Philadelphia

Popular Test Prep

GMAT Test Prep in Houston, SAT Test Prep in Seattle, ISEE Test Prep in Philadelphia, ISEE Test Prep in San Diego, ACT Test Prep in Dallas Fort Worth, SAT Test Prep in Los Angeles, SSAT Test Prep in Chicago, MCAT Test Prep in Dallas Fort Worth, ACT Test Prep in Phoenix, SSAT Test Prep in San Diego

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

SAT Math : How to find the solution to an inequality with addition

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

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

Example Question #4 : How To Find The Solution To An Inequality With Addition

Example Question #5 : How To Find The Solution To An Inequality With Addition

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

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

Example Question #21 : Inequalities

Example Question #5 : How To Find The Solution To An Inequality With Addition

Example Question #6 : How To Find The Solution To An Inequality With Addition

Example Question #23 : Inequalities

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

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: