From the four inequalities $2x > 70$, $x < 25$, $x > 5$, and $x > 5$, two are true and two are false. Find the value of $x$, given that it is an integer.
Given that $x$ is an integer, the inequalities can be rewritten as: $x>35, x>6$ and $x>5$. If it is not true that $x>5, x>6$ and $x>35$ - one is true and two are false.

Since the third inequality implies the first two, and the second implies the first, there is only one option: the first inequality is true, and the other two are false. Therefore, $5<x \leq 6$, which means $x=6$.

## Answer

$x=6$.