Solve the inequality x(x+2)>8 for x.

x(x+2)>8 if and only if x^2+2x-8>0 if and only if (x+4)(x-2)>0. There are three cases: x<-4, -4 In the first case x+4<0 and x-2<0, so their product is positive: (x+4)(x-2)>0. Next x+4>0 and x-2<0, so their product is negative: (x+4)(x-2)>0. Finally x+4>0 and x-2>0, so their product is positive: (x+4)(x-2)>0. Hence the solutions are in the first and third cases when x<-4 or 2

Answered by Joshua T. Maths tutor

3461 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Integrate ln(e^x)


Differentiate with respect to x: 4(x^3) + 2x


Find the derivative of f(x)=x^3 sin(x)


integrate from 0 to 2: 2x*sqrt(x+2) dx


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