$x - 7>8$
Now if we simplify this expression, we get $x>15$. So that means that the value of any number (i.e. $x$), is greater than $15$, right? But what if I substitute $x = 4$? Or $x=5$? Or any number that is less than $15$? What can we say about that?
On
If someone makes the assertion that $x - 7 > 8,$ then they have implicitly asserted that $x$ is not just "any number." They have implied that $x$ is a number greater than $15.$
But it is not usual in mathematical writing for someone to start out with a statement such as $x - 7 > 8$ without any previous explanation. There is usually something beforehand (or sometimes soon afterward) that explains how to interpret the symbol $x$ in that particular occurrence of that particular formula. If you really want to know what to say about the inequality $x - 7 > 8,$ you have to consider what came before and after it.
The equality $$x-7>8$$ holds if and only if $$x>15$$ so if and only if $x$ is greater than $15$ . If you insert a real number $x\le 15$, then $x-7>8$ does not hold. For example, $x=4$ gives the false statement $-3>8$.