Solve the equation x=4-|2x+1|

We can start by rearranging the equation such that the modulus (also called the absolute value) is the only component on the right-hand-side of the equation.

This gives us: x-4=-|2x+1| (by subtracting 4 from each side) and we shall call this equation (1)

The modulus of a number may be thought of as its distance from zero e.g. |x|=x for a positive x, |x|=-x for a negative x.

Therefore, equation (1) can be written as two separate equations:

x-4=-(2x+1)   (2)   &   x-4=(2x+1)   (3)

We can now rearrange equation (2) and solve for x as follows:

x-4=-2x-1   (we can then plus 2x to each side)

3x-4=-1      (we can then plus 4 to each side)

3x=3           (we can then divide each side by 3)


We will now do the same with equation (3):

x-4=2x+1   (we can then minus x from each side)

-4=x+1       (we can then minus 1 from each side)


We have now solved the equation x=4-|2x+1| and found that the values of x which satisfy this equation are x=1 and x=-5.

Benjamin C. GCSE Maths tutor, 11 Plus Maths tutor, A Level Maths tuto...

1 year ago

Answered by Benjamin, an A Level Maths tutor with MyTutor

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


£22 /hr

Ruth N.

Degree: Economics (Bachelors) - Cambridge University

Subjects offered:Maths, Economics+ 2 more

-Personal Statements-
-Oxbridge Preparation-

“Economics Graduate from Cambridge, wanting to share my passion for the discipline”

£20 /hr

Harry C.

Degree: General Engineering (Masters) - Durham University

Subjects offered:Maths, Physics+ 1 more

Further Mathematics

“Second year Engineering student, I'm passionate, dedicated and personable. A- Level Maths and Physics (A*AA).”

MyTutor guarantee

£24 /hr

Sophie H.

Degree: Mathematics (Masters) - Bristol University

Subjects offered:Maths, Further Mathematics

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.”

About the author

Benjamin C.

Currently unavailable: for regular students

Degree: Financial Mathematics (Masters) - Exeter University

Subjects offered:Maths


“About Me:I have recently graduated from the Univeristy of Exeter with a degree in BSc. Mathematics. I am passionate about maths, and helping others understand and gain confidence in themselves is a rewarding experience and why I enjo...”

You may also like...

Other A Level Maths questions

The quadratic equation 2x^2+8x+1=0 has roots a and b. Write down the value of a+b and ab and a^2+b^2.

Find the sum and product of the roots of the equation 2x^2+3x-5=0

How do I sketch the graph y = (x^2 + 4*x + 2)/(3*x + 1)

Why bother with learning calculus?

View A Level Maths 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