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Definition of Sets

Find P∩ Q a...

Question

Find $P \cap Q$ and represent on the number line
$P = {x : 8 x - 1 > 5 x + 2, x \in N}$ and $Q = {x : 7 x \geq 3 (x + 6), x \in N}$

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Solution

$\begin{matrix} P = x : 8 x - 1 > 5 x + 2, x \in N a n d Q = x : 7 x > 3 x + 18 \Rightarrow 8 x - 1 > 5 x + 2 \Rightarrow 7 x > 3 x + 18 \Rightarrow 3 x > 3 \Rightarrow 4 x > 18 x > 1 x > \frac{9}{2} ∴ P \cup Q = (\frac{9}{2}, \propto) \end{matrix}$

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