How do I solve equations with modulus functions on both sides?

MYTUTOR SUBJECT ANSWERS

Answers / Maths / A Level / How do I solve equations with modulus functions on both sides?

892 views

How do I solve equations with modulus functions on both sides?

Whilst it is possible to do it algebraically, it's usually easier to solve it graphically. For example: for which values of x is |x+2| = |3x-6|. By sketching the graphs of y=|x+2| and y=|3x-6|, it is easy to see that there are 2 intersections: one for positive values of x+2 and negative values of 3x-6, the other for positive values of x+2 and positive values of 3x-6. To find the first x value solve x+2 = -3x+6, to find the second x value solve x+2 = 3x-6.

If you prefer to work algebraically, simply ask "for which values of x is x+2 negative, and for which is it positive". Do the same for 3x-6. Now solve for x in each section (with the 3 sections being: both negative, one positive one negative, both positive). Check each value you've found to see if it makes sense. Demonstrated below.

For both negative:
-x-2 = -3x+6, x<-2
x = 4, x<-2. This is a clear contradiction, so we ignore this value.

For x+2 positive and 3x-6 negative:
x+2 = -3x+6, -2 x = 1, -2

For both positive:
x+2 = 3x-6, 2 x = 4, 2

Therefore the answer to |x+2| = |3x-6| is x = 1, x = 4

Seb G. 11 Plus Maths tutor, 13 plus Maths tutor, A Level Maths tutor...

11 months ago

Answered by Seb, an A Level Maths tutor with MyTutor

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

354 SUBJECT SPECIALISTS

Scott R. GCSE Maths tutor, 13 Plus Maths tutor, A Level Maths tutor,...

View profile

£26 /hr

Scott R.

Degree: PGCE Secondary Mathematics (Other) - Leeds University

Subjects offered:Maths, Further Mathematics

“I am currently completing 2 PGCEs in Leeds. I have always had a passion for maths and my objective is to help as many as possible reach their full potential.”

5.0

35 reviews | 95 completed tutorials

Save profile

Leon P. 13 Plus Maths tutor, GCSE Maths tutor, IB Maths tutor, A Lev...

View profile

£22 /hr

Leon P.

Degree: Mathematics (Bachelors) - Imperial College London University

Subjects offered:Maths

“21 years old. 2 years experience teaching. BSc Mathematics Imperial College London. Studying MSc in Aerospace Dynamics (please ask for references).”

5.0

2 reviews | 2 completed tutorials

Save profile

Sophie H. A Level Maths tutor, GCSE Maths tutor

View profile

£24 /hr

Sophie H.

Degree: Mathematics (Masters) - Bristol University

Subjects offered:Maths, Further Mathematics

“I’ll help anyone finding maths hard. I still struggle now, it's not meant to be easy! Be at my tutorial or (c^2-a^2) <- a maths joke, I apologise.”

5.0

31 reviews | 63 completed tutorials

Save profile

See more A Level Maths tutors

About the author

View profile

Seb G.

Currently unavailable: for regular students

Degree: Mathematics (Masters) - Bath University

Subjects offered:Maths

“Me: I'm a second year maths student at the University of Bath. I fell in love with maths after a rocky start with the subject, so believe that I can help people regardless of whether they like maths or not. I've been tutoring maths l...”

MyTutor guarantee

Save profile

Version:	3.49.1
Build:	7666049797d9
Time:	2017-08-13T14:18:20Z

MYTUTOR SUBJECT ANSWERS

How do I solve equations with modulus functions on both sides?

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

354 SUBJECT SPECIALISTS

About the author

You may also like...

Posts by Seb

Other A Level Maths questions

One-to-one help is at your fingertips