The solution set for the following inequation is:
−x3≤x2−113<16, xϵR
Given: −x3≤x2−113<16
⇒−x3≤3x−86 and 3x−86<16
Rule: If both the sides of an inequation are multiplied or divided by the same positive number, then the sign of the inequality will remain the same.
On multiplying left hand side inequation by 6 and right hand side inequation by 6 in both the inequations, we get;
⇒−2x≤3x−8 and 3x−8<1
⇒8x≤3x+2x and 3x<1+8
⇒8≤5x and 3x<9
⇒{85≤x<3,xϵR}.