Inequalities — Important Questions

{..., -2, -1, 0, 1, 2}

Add 5 to both sides: -10 < -5 + 2x ⇒ -5 < 2x. Divide by 2: x > -2.5. For integers, all integers greater than -2.5 are {..., -2, -1, 0, 1, 2}.

{1, 2, 3, 4}

Add 8 to both sides: 3x - 8 < 7 ⇒ 3x < 15 ⇒ x < 5. For natural numbers, the values are 1, 2, 3, and 4.

{0, 1, 2, 3, 4, ...}

Subtract 5: 4x + 5 ≥ 1 ⇒ 4x ≥ -4 ⇒ x ≥ -1. Whole numbers are 0, 1, 2, 3, 4, ... , so every whole number works.

{-2, -1, 0, 1}

The integers must be at least -2 and less than 2. That gives -2, -1, 0, and 1. The number 2 is excluded because the inequality is strict at the upper end.