Solve as directed : Convert to linear inequality and solve for natural numbers:
(x-2) (x-3) `lt` (x +3) (x-1)

Explanation

(x-2) (x-3) `lt` (x +3) (x-1)
`rArr x^2 - 5x + 6 lt x^2 + 2x-3`
`rArr -5x + 6 lt 2x - 3`
`rArr -5x - 2x lt -3 -6
`rArr -7x lt -9
`rArr x gt 9/7`
If x `in` N the solution set is S = { 2,3,4…….}