Not including rational number in inequality

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If you have a linear inequality like $x < 7$ where $x$ belongs to rational numbers. Then on graphing it on a number line, a unfilled circle is used to denote that $7$ is not included.

But that means that $x = 6.99999\dots$ at max but $7$ is not included.

$0.99999\dots = 1$ (sources - wikipedia) and therefore, $6.99999\dots = 7$.

So although you are not including $7$ in the solution set of inequality, $7$ is still a solution.

How is that possible? Am I going wrong somewhere?