Question

Solve the inequation:

3 – 2x ≥ x – 12 given that x ∈ N.

Answer 1

3 – 2x ≥ x – 12

Rearrange the terms by bringing all variables to one side and constants to the other. Add 2x to both sides and add 12 to both sides:

3 + 12 ≥ x – 2x

15 ≥ 3x

Divide both sides by 3 to isolate x:

`15/3 >= x`

5 ≥ x ⇒ x ≤ 5

We are given that x ∈ {N} (Natural numbers). Remember that natural numbers are positive integers starting from 1 (1, 2, 3, 4, ...).

The values of x that are natural numbers and less than or equal to 5 are:

x = 1, 2, 3, 4, 5