Which of the following inequalities have at least one positive solution and at least one negative solution? Indicate all such inequalities.
(A) 5/3 x < x
(B) x^3 < x
(C) x - 6 < x – 7

• Let us consider the inequality symbol as a normal '='(equal to) but if we multiply/Divide by '-'(minus) both sides then invert the inequality symbol.
  First step, grab all values and variables to left hand side.
  Next check whether it is +ve or -Ve or both.
  (A) (5X/3) < X
  (5X/3)-X < 0
  X[(5/3)-1]if x^2-1 < 0, then x^2 < 0+1 => x^2 < 1. Since x is always squared, it is always +ve.
  So this equation has both +ve and -ve solution for X.
  
  (C) x-6 < x-7
  x-6-x-7 < 0
  -6-7
• 7 years agoHelpfull: Yes(0) No(0)