Solve `3x + 8 > 2`, when
(i) x is a natural number.
(ii) x is an integer

Answer

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

(ii) `(-2, oo)`

Explanation

`3x + 8 > 2`
`implies 3x > 2-8`

`implies 3x > -6`

`implies (3x)/3 > (-6)/3`

`implies x > -2`

(i) The integers greater than -2 are `-1, 0, 1, 2, ...`.

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

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

...