Alevel edexcel maths question

Just expand the squared term and simplify. It should drop out so upload your working if not.

Your inequality is the wrong way round. Where did you use the info that x<0?

Your inequality is the wrong way round. Where did you use the info that x<0?

Is the x<0 applied to the right side of the equation only?

x being negative is a property of the variable, you cant just apply it to one side, whatever that means.

Youve nearly got the inequality, just think how might it being > < be determined by the sign of x?

You get to the 2xy<8x^2, then because x is less than 0, it is a negative number meaning both sides would be -2xy<-8x^2.
Divide through by x. -2y<-8x, and times both sides by -1, and when you do this you have to flip the inequality sign.
Then you get 2y>8x, and divide by 2, y>4x.

You should have flipped the inequality 3 times using this, but youve only done it one time?

Why's that?

You multiply/divide by a negative number 3 times. Even just thinking about your first line
2xy<8x^2
If you take terms over (so forget about multiplying by -1) you should get
-8x^2 < -2xy