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Worked Examples · Example 5

Q.Solve 5−2x≥15-2x\ge 1 where xx is a natural number, and list the solution set.

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Solve over the reals first. Subtract 55:

5−2x≥1 ⇒ −2x≥−4.5-2x\ge 1\ \Rightarrow\ -2x\ge -4.

Divide by −2-2 — a negative number, so the sign reverses from ≥\ge to ≤\le:

x≤2.x\le 2.

Apply the domain. Here xx must be a natural number (x∈N={1,2,3,… }x\in\mathbb{N}=\{1,2,3,\dots\}). The natural numbers satisfying x≤2x\le2 are only

x=1 and x=2.x=1\ \text{and}\ x=2. …

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