Is decimal part of inequality whole number?

Question

If you have an inequality, x is "greater than -7" but "less than -5."
Is -6 the only number that will satisfy this inequality, or will there be multiple solutions (e.g. -5.5, -6.5, etc)?
In other words, are decimals included in the whole numbers of inequalities?

Thank you!

Answer 1

You're given $-7 < x < -5$.

If you're told that $x$ is an integer, then only $x = -6$ will satisfy the inequality.

If you're not told that, then $x$ can be any real number. Which means numbers like $-5.5, -6.5, -5.523432423,, -6.33333.... (= -\frac{19}{3}), -(6 + \frac{\sqrt 2}{2}), -(5+\frac{\pi}{4}), -(5 + \frac{e}{2})$, etc. all satisfy the inequality along with an infinite number of other possibilities.