Solve `5x-3<3x+1` when (i) x is an integer, (ii) x is a real number.

Explanation

We have` 5x−3<3x+1`

⇒`5x−3+3<3x+1+3`

⇒`5x<3x+4`

⇒`5x−3×<3x+4−3x`

⇒`2x<4⇒x<2`

(i) When x is an integer the solutions of the given inequality are `{...,−4,−3,−2,−1,0,1...}`

(ii) When x is a real number the solutions of the inequality are given by x < 2 i.e. all real number x which are less than 2 Therefore the solution set of the inequality is `x in (−oo,2)`