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

7025 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Let f(x)= x^3 -9x^2 -81x + 12. Calculate f'(x) and f''(x). Use f'(x) to calculate the x-values of the stationary points of this function.


Use the substitution u=2+ln(t) to find the exact value of the antiderivative of 1/(t(2+ln(t))^2)dt between e and 1.


Why do the trig addition formulae work?


How do you differentiate parametric equations?


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