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Real Numbers

Solve: 3x-1≤...

Question

Solve: $3 (x - 1) \leq 2 (x - 3)$ when $x$ is an real number.

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Solution

$3 (x - 1) \leq 2 (x - 3)$
$\Rightarrow 3 x - 3 \leq 2 x - 6$
$\Rightarrow 3 x - 3 + 3 \leq 2 x - 6 + 3$
$\Rightarrow 3 x \leq 2 x - 3$
$\Rightarrow 3 x - 2 x \leq 2 x - 3 - 2 x$
$\Rightarrow x \leq - 3$
$∴ x \in (- \infty, - 3]$

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