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.

Answered by Joe C. Maths tutor

6926 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I remember the coefficients of a Taylor expansion?


How do I find the integral ∫(ln(x))^2dx ?


p(x)=2x^3 + 7x^2 + 2x - 3. (a) Use the factor theorem to prove that x + 3 is a factor of p(x). (b) Simplify the expression (2x^3 + 7x^2 + 2x - 3)/(4x^2-1), x!= +- 0.5


Integrate xsin(x) with respect to x


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences