[ [ Linear inequalities and systems of inequalities] ]

The number x is natural. Among the statements

1) $2 x>70$,
2) $x>100$,
3) $3 x>25$,
4) $x \geq 10.5$,
5) $x>5$ three are true and two are false. What is the value of $x$?
Write down all inequalities with respect to $x$.

## Solution

Let's write the first and third inequalities as $x>35, x>25 / 3$. We will mark the numbers $5, 25 / 3, 10, 35$, 100 on the number line; these points divide the line into six intervals (two of which are infinite). It remains to consider all intervals and find the one that satisfies the condition of the problem.

## Answer

$x=9$.