MYTUTOR SUBJECT ANSWERS

579 views

Solving absolute value inequality

For which values of x does the following inequality hold true:

 

(|x|+2)/(|x|-3) < 4

The first thing we want to do is eliminate the fraction on the left-hand side (LHS) of the equation. We do so by multiplying both side by |x|-3, leading to:

 

|x|+2 < 4(|x|-3)

We can simplify the right-hand side (RHS):

|x| + 2 < 4|x| - 12

We now want to group like terms together. As such, we will move all |x| terms to the RHS, and all integer terms to the LHS.

2 + 12 < 4|x| - |x|

14 < 3|x|

We now divide both sides by 3 to eliminate the coefficient of |x|

14/3 < |x|

or

|x| > 14/3

 

Now, imagine a number line...

 

<---- -x ------- 0 ----- x --------->

I would like you to remember the definition of |x| (absolute value) which indicates the distance of a value x from 0. (In other words, it makes any negative number positive and leaves any positive number positive)

This suggests that any x > 14/3 will satisfy |x| > 14/3.

However, we also have to remember that any value inferior to -14/3 will also satisfy the inequality.

As such, we solve the solution as

x > 14/3 OR x < -14/3

 

Dario P. A Level Computing tutor, Mentoring Computing tutor, IB Compu...

3 years ago

Answered by Dario, an IB Italian tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

11 SUBJECT SPECIALISTS

£30 /hr

Marcella M.

Degree: Psychology and neuroscience (Bachelors) - Cambridge University

Subjects offered:Italian, Psychology+ 4 more

Italian
Psychology
Extended Project Qualification
English Language
-Personal Statements-
-Oxbridge Preparation-

“Cambridge University student with a passion for learning and interested in making it enjoyable and productive for everyone!”

MyTutor guarantee

|  2 completed tutorials

£26 /hr

Michelangelo M.

Degree: MMath Mathematics with Placement (Masters) - Bath University

Subjects offered:Italian, Maths+ 4 more

Italian
Maths
Further Mathematics
Computing
.STEP.
.MAT.

“Mathematics student at the University of Bath, willing to help you love this subject and improve your grades.”

£36 /hr

Dario P.

Degree: Computer Science (Masters) - Manchester University

Subjects offered:Italian, Maths+ 3 more

Italian
Maths
ICT
Computing
-Personal Statements-

“I am Computer Science Russell Group student with experience in research and industry and strong mathematical skills, I enjoy tutoring and helping students consolidate their knowledge.”

About the author

£36 /hr

Dario P.

Degree: Computer Science (Masters) - Manchester University

Subjects offered:Italian, Maths+ 3 more

Italian
Maths
ICT
Computing
-Personal Statements-

“I am Computer Science Russell Group student with experience in research and industry and strong mathematical skills, I enjoy tutoring and helping students consolidate their knowledge.”

You may also like...

Other IB Italian questions

How do I use "Essere" and "Avere" in the perfect tense?

How do you form conditional sentences (periodo ipotetico) in Italian?

What can I do to improve my Italian reading skills in order to pass my exam with flying colours?

Solving absolute value inequality

View IB Italian tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok