Solve $5 x - 3 \leq 3 x + 1$ when $x$ is an integer.

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Solution

$5 x - 3 \leq 3 x + 1$

$\Rightarrow 5 x - 3 + 3 \leq 3 x + 1 + 3$
$\Rightarrow 5 x \leq 3 x + 4$
$\Rightarrow 5 x - 3 x \leq 3 x + 4 - 3 x$
$\Rightarrow 2 x \leq 4$
$\Rightarrow x \leq 2$
When $x \in I,$ the solution set is ${, . . . ., - 2, - 1, 0, 1, 2,}$

i.e. $x \in (- \infty, 2]$ for $x \in I$

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