5.1 Introduction to Inequalities

Simplify: Divide both sides by 30. $x < \frac{200}{30} \implies x < \frac{20}{3} \implies x < 6.66...$

Case (i): x is a natural number ($\mathbb{N}$) The natural numbers less than 6.66 are $\{1, 2, 3, 4, 5, 6\}$. Solution Set: $\{1, 2, 3, 4, 5, 6\}$.

Case (ii): x is an integer ($\mathbb{Z}$) The integers less than 6.66 include all negative integers, zero, and positive up to 6. Solution Set: $\{..., -3, -2, -1, 0, 1, 2, 3, 4, 5, 6\}$.