Question 308695
I. False. For example, let x = -10 and z = -1. Clearly {{{x>z}}} is false. If we let {{{y=-5}}}, then {{{xy=-10(-5)=50>1}}} showing that {{{xy>1}}} is true.



II. False, this is only true if {{{xyz<z}}}. So {{{xyz < -1}}} is on the right track, but it is false. For example, if {{{xy=2}}}, and we let {{{z=-1/2}}}, then {{{xyz=2(-1/2)=-1}}} which is clearly not less than -1. We must make the requirement that the right side be 'z' and not -1.


III. This is true since dividing both sides of an inequality by a negative number will flip the inequality sign. Basically, divide both sides of {{{xy > 1}}} by the negative number 'z' to get {{{(xy)/z < 1/z}}} (don't forget to flip the sign).