Solve the inequality x < 4 - |2x + 1|.

In order to deal with the modulus sign, we must take account of 2 possible cases:

Case 1: |2x + 1| = (2x +1). In this case we can solve algebraicly, preserving the inequality sign, to get that x < 4 -(2x + 1) = 3 - 2x. Then by adding 2x to each side and dividing both sides by 3 we get x < 1.

Case 2: |2x + 1| = -(2x +1). In this case we solve algebraicly again so that x < 4 + (2x +1) = 2x + 5. Hence by subtracting a 5 and an x from each side we get x > -5.

Finally we combine the results of each case, namely that x < 1 and x > -5 to get -5 < x < 1 as our final solution.

Joe C. A Level Maths tutor, GCSE Maths tutor

6 months ago

Answered by Joe, an A Level Maths tutor with MyTutor

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


£20 /hr

Joe C.

Degree: General Engineering (Masters) - Durham University

Subjects offered: Maths, Science+ 2 more


“Masters student at Durham University, ready to help you excel at Maths and Science ”

£20 /hr

George S.

Degree: Physics (Masters) - Birmingham University

Subjects offered: Maths, Physics+ 2 more

Further Mathematics

“About Me: I am just entering my first year to study Physics at University of Birmingham, I've always enjoyed anything maths based hence my A-level choices, I hope I can help you through your work whether it's GCSE or A-level and maybe...”

£20 /hr

James C.

Degree: Theoretical Physics (Masters) - Durham University

Subjects offered: Maths, Physics


“About Me: I'm a physics student in my fourth year at Durham University. I have always loved the neatness and completeness of science and maths, and this is something that I want to help other people to discover. I have previously tuto...”

About the author

£26 /hr

Joe C.

Degree: Mathematics (Masters) - Bristol University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“I'm a third year student at Bristol University studying a Masters Degree in Mathematics. I try to make my tutorials engaging, and tailor them to your individual needs so that we are working towards the grade you aspire to achieve! I'v...”

You may also like...

Posts by Joe

Find the exact value of the gradient of the curve y = e^(2- x)ln(3x- 2). at the point on the curve where x = 2.

Solve the inequality x < 4 - |2x + 1|.

Other A Level Maths questions

Find the stable points of the following function, determine wether or not they are maxima or minima. y= 5x^3 +9x^2 +3x +2

Solve simultaneously: x + y + 3 = 0 and y = 2x^2 +3x - 1

Find the values of x that satisfy the following inequality 3x – 7 > 3 – x

How do I find the minimum or maximum of a quadratic function?

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