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Solving Equations with Linear Expressions on One Side and Numbers on the Other Side

Solve: 3x-7>...

Question

Solve: $3 x - 7 > 5 x - 1$ when $x$ is a natural number.

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Solution

$3 x - 7 > 5 x - 1$
$\Rightarrow 3 x - 7 + 7 > 5 x - 1 + 7$
$\Rightarrow 3 x > 5 x + 6$
$\Rightarrow 3 x - 5 x > 5 x + 6 - 5 x$
$\Rightarrow - 2 x > 6$
$\Rightarrow x < - 3$
$∴ x \in ϕ$

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