How to solve the absolute-value inequalities?

Absolute value means how far away you are from zero. It's better to draw a number line to understand and solve the question. 

Given the inequality l 4x+3 l >15 , the distance of the 4x+3 value from 0 must be greater than 15, so 4x+3 has to be either greater than 15 or less than -15 (negative 15). so it becomes

4x+3 > 15 or 4x+3< -15

Then subtract 3 from both sides, 4x >12 or 4x < -18, 

divided by 4 , so the inequalities become x > 3 or x < -9/2 which are the solutions. 



Cynthia C. GCSE Maths tutor, A Level Maths tutor, A Level Mandarin tutor

2 years ago

Answered by Cynthia, an A Level Maths tutor with MyTutor

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


£20 /hr

Becky L.

Degree: Economics (Bachelors) - Warwick University

Subjects offered: Maths, Economics


“Hi, I'm Becky and I'm a second year Economics student at the University of Warwick!  About Me I've always loved Maths, but am also pretty creative, too - I think that's why I decided to study economics. I did the 11+, got good grades...”

£20 /hr

Kyle R.

Degree: Mathematics (Masters) - Oxford, Corpus Christi College University

Subjects offered: Maths, Further Mathematics + 2 more

Further Mathematics

“Hi! I'm Kyle, a 2nd year Oxford undergraduate studying Maths at Corpus Christi College. I aim to be an understanding and friendly face, whilst being thorough with the material I cover. I've acheived A* grades in Maths, Further Maths a...”

£20 /hr

Isabel R.

Degree: Mathematics (Bachelors) - Manchester University

Subjects offered: Maths, Physics+ 1 more

Further Mathematics

“I am currently a first year studying Mathematics at the University of Manchester-so A Levels and GCSEs are still fresh in my mind when it comes to remembering how I learnt the material myself. In school I mentored GCSE students in Mat...”

MyTutor guarantee

About the author

£20 /hr

Cynthia C.

Degree: Environmental Science (Bachelors) - Nottingham University

Subjects offered: Maths, Mandarin


“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Other A Level Maths questions

How can we determine stationary points by completing the square?

Solve for 0<=θ<π, the equation sin3θ-(sqrt3)cosθ=0 (C2)

Solve algebraically: 2x - 5y = 11, 3x + 2y = 7

Find the tangent to the curve y=x^3+3 at the point x=1.

View A Level Maths tutors


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