Call Now to Set Up Tutoring:

(888) 888-0446

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

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 #11 : How To Find The Solution To An Inequality With Subtraction

$\dpi{100} \small -2y+7>-7+y$

Given the inequality above, which of the following MUST be true?

Possible Answers:

$\dpi{100} \small y>\frac{-14}{3}$ $y>\textup{2}$

$\dpi{100} \small y<5$ $y< \textup{3}$

$\dpi{100} \small y>\frac{14}{3}$

$\dpi{100} \small y>-5$ $y < \textup{5}$

$\dpi{100} \small y<\frac{-14}{3}$

Correct answer:

$\dpi{100} \small y>-5$ $y < \textup{5}$

Explanation:

$\dpi{100} \small -2y+7>-7+y$ Subtract from both sides:

-2y+7-y>-7+y-y

-3y+7>-7

Subtract 7 from both sides:

-3y+7-7>-7-7

-3y>-14

Divide both sides by $\dpi{100} \small -3$ :

$\frac{-3y}{-3}>\frac{-14}{-3}$

Remember to switch the inequality when dividing by a negative number:

$y<\frac{14}{3}$

Since $\dpi{100} \small y<\frac{14}{3}$ is not an answer, we must find an answer that, at the very least, does not contradict the fact that is less than (approximately) 4.67. Since any number that is less than 4.67 is also less than any number that is bigger than 4.67, we can be sure that is less than 5.

Report an Error

Example Question #1 : Inequalities

A factory packs cereal boxes. Before sealing each box, a machine weighs it to ensure that it is no lighter than 356 grams and no heavier than 364 grams. If the box holds grams of cereal, which inequality represents all allowable values of ?

Possible Answers:

$\left | w-360 \right |=4$

$\left | w+360 \right |\geq4$

$\left | w+360 \right |<4$

$\left | w-360 \right |\leq4$

$\left | w-360 \right |>4$

Correct answer:

$\left | w-360 \right |\leq4$

Explanation:

The median weight of a box of cereal is 360 grams. This should be an allowable value of w. Substituting 360 for w into each answer choice, the only true results are:

$\\ |w -360| \leq 4 \\ |360 -360| \leq 4 \\0 \leq 4$

and:

$\\|w + 360| \geq 4 \\ |360 + 360| \geq 4\\ 720 \geq4$

Notice that any positive value for w satisfies the second inequality above. Since w must be between 356 and 364, the first inequality above is the only reasonable choice.

Report an Error

Example Question #11 : How To Find The Solution To An Inequality With Subtraction

Solve for .

$4x-8\geq 28$

Possible Answers:

x<9

x>9

x=9

$x\leq 9$

$x\geq 9$

Correct answer:

$x\geq 9$

Explanation:

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

$4x-8\geq 28$ Add on both sides.

$4x\geq 36$ Divide on both sides.

$x\geq 9$

Report an Error

Example Question #13 : Inequalities

Solve for .

-9x-38>25

Possible Answers:

x>-7

x<-7

$x\geq -7$

$x\leq -7$

x=-7

Correct answer:

x<-7

Explanation:

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

-9x-38>25 Add on both sides.

-9x>63 Divide on both sides. Remember to flip the sign.

x<-7

Report an Error

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

Solve for .

7x-27<9x-77

Possible Answers:

x>-25

x>25

x<25

x>50

x<50

Correct answer:

x>25

Explanation:

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

7x-27<9x-77 Add and subtract on both sides.

50<2x Divide on both sides.

25<x

Report an Error

Example Question #14 : How To Find The Solution To An Inequality With Subtraction

Solve for .

$\left | 6x-45\right |\leq 75$

Possible Answers:

$5\leq x\leq 20$

$-5\leq x\leq 20$

$x\leq 20$

$-5\leq x$

$x\geq 20, x\leq -5$

Correct answer:

$-5\leq x\leq 20$

Explanation:

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

$\left | 6x-45\right |\leq 75$ We need to set-up two equations since its absolute value.

$6x-45\leq 75$ Add on both sides.

$6x\leq 120$ Divide on both sides.

$x\leq 20$

$-(6x-45)\leq 75$ Divide on both sides which flips the sign.

$6x-45\geq -75$ Add on both sides.

$6x\geq -30$ Divide on both sides.

$x\geq -5$

Since we have the 's being either greater than or less than the values, we can combine them to get $-5\leq x\leq 20$ .

Report an Error

Example Question #16 : Inequalities

Solve for .

$\left | 5x-75\right |>45-x$

Possible Answers:

7.5<x<20

x>20

x>7.5

-20<x<-7.5

x>7.5, x>20

Correct answer:

x>20

Explanation:

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

$\left | 5x-75\right |>45-x$ We need to set-up two equations since it's absolute value.

5x-75>45-x Add x, 75 on both sides.

6x>120 Divide on both sides.

x>20

-(5x-75)>45-x Distribute the negative sign to each term in the parenthesis.

-5x+75>45-x Add and subtract on both sides.

30>4x Divide on both sides.

7.5>x We must check each answer. Let's try .

$\left | 10(5)-75\right |>45-10$ 25>35 This is not true therefore 7.5>x is not correct. Let's try .

$\left | 5(30)-75\right |>45-30$ 75>15 This true so therefore x>20 is correct.

Final answer is x>20 .

Report an Error

Example Question #15 : How To Find The Solution To An Inequality With Subtraction

Solve for .

$\left | x-19\right |<2x-26$

Possible Answers:

7<x

15<x

x< 15

7<x, 15<x

7<x<15

Correct answer:

15<x

Explanation:

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

$\left | x-19\right |<2x-26$ We need to set-up two equations since it's absolute value.

x-19<2x-26 Subtract and add on both sides.

7<x

-(x-19)<2x-26 Distribute the negative sign to each term in the parenthesis.

-x+19<2x-26 Add , on both sides.

45<3x Divide on both sides.

15<x We must check each answer. Let's try .

$\left | 10-19\right |<2(10)-26$ 9<-6 This is not true therefore 7<x is not correct. Let's try .

$\left | 20-19\right |<2(20)-26$ 1<20 This true so therefore 15<x is correct.

Final answer is 15<x .

Report an Error

View SAT Mathematics Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

View SAT Mathematics Tutors

Clinton
Certified Tutor

Rensselaer Polytechnic Institute, Current Undergrad, Biology, General. Albany Medical College, PHD, Molecular and Cellular Ph...

View SAT Mathematics Tutors

Sharif
Certified Tutor

NCCU, Bachelors, Physics and Mathematics.

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

GRE Courses & Classes in Chicago, LSAT Courses & Classes in Philadelphia, ACT Courses & Classes in Denver, MCAT Courses & Classes in Phoenix, SSAT Courses & Classes in San Diego, LSAT Courses & Classes in Boston, ISEE Courses & Classes in Denver, ISEE Courses & Classes in Philadelphia, ISEE Courses & Classes in Washington DC, MCAT Courses & Classes in Washington DC

Popular Test Prep

SAT Test Prep in Atlanta, ACT Test Prep in Miami, SSAT Test Prep in San Diego, ISEE Test Prep in New York City, ISEE Test Prep in Philadelphia, GRE Test Prep in Los Angeles, GRE Test Prep in San Diego, LSAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Chicago, LSAT 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 subtraction

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #11 : How To Find The Solution To An Inequality With Subtraction

Example Question #1 : Inequalities

Example Question #11 : How To Find The Solution To An Inequality With Subtraction

Example Question #13 : Inequalities

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

Example Question #14 : How To Find The Solution To An Inequality With Subtraction

Example Question #16 : Inequalities

Example Question #15 : How To Find The Solution To An Inequality With Subtraction

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: