Solve `5x - 3 < 7`, when
(i) x is a natural number.
(ii) x is an integer

Answer

(i) `{...,-4, -3, -2, -1, 0, 1}`

(ii) `(-oo, 2)`

Explanation

`5x - 3 < 7`

`implies 5x < 7 + 3`

`implies 5x < 10`

`implies (5x)/5 < 10/5`

`implies x < 2`

(i) The integers less than 2 are `...,-4, -3, -2, -1, 0, 1`.

Thus, when `x` is an integer, the solutions of the given inequality are `...,-4, -3, -2, -1, 0, 1`.

Hence, in this case, the solution set is `{...,-4, -3, -2, -1, 0, 1}`.

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