Which of these are equivalent?

Question

I. x > -3

 

II. x-4 < -8

 

III. -2x < 8

 

(a) I and I only

(b) I and III only

(c) I, II, and III

(d) none of them

Answer 1

I. x > -3

II. x-4 < -8  i.e. x < -4 (because of adding four to each side)

III. -2x < 8  i.e. x > -4 (because division by -2 requires reversal of direction of the inequality symbol)

 

So you see each inequality is different.