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Solve: 4x+3≤...

Question

Solve: $4 x + 3 \leq 6 x + 7$ when $x$ is a natural number.

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Solution

$4 x + 3 \leq 6 x + 7$
$\Rightarrow 4 x + 3 - 3 \leq 6 x + 7 - 3$
$\Rightarrow 4 x \leq 6 x + 4$
$\Rightarrow 4 x - 6 x \leq 6 x + 4 - 6 x$
$\Rightarrow - 2 x \leq 4$
$\Rightarrow - x \leq 2$
$\Rightarrow x \geq - 2$
$∴ x \in N - {- 2, - 1, 0}$

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