If the replacement set is the set of natural numbers (N), find the solution set of the inequality $8 - 2 x \geq x - 5$ .

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Solution

$8 - 2 x \geq x - 5; x$ ∈ N
$\Rightarrow 8 + 5 \geq 2 x + x$
$\Rightarrow 13 \geq 3 x \Rightarrow 3 x \leq 13$
$\Rightarrow x \leq \frac{13}{3}$
$\Rightarrow x = 1, 2, 3, 4 (x \in N)$
$∴ S o l u t i o n s e t = 1, 2, 3, 4$

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