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Ballparking: Overview

If $$\frac{1}{x-3} > \frac{5}{8}$$, which of the following can be the value of $$x$$?
Good work! [[snippet]] Since $$\frac{5}{8}$$ is positive, $$\frac{1}{x-3}$$ is greater than a positive number, which means $$\frac{1}{x-3}$$ itself has to be positive. Thus, $$x-3$$ itself must be positive, which means that $$x > 3$$. Now that's a wide ballpark, but you can still __POE__ answers that are out of the ballpark. Answer choice A, $$\frac{16}{5} = 3.2$$, is the only answer choice that is greater than 3. Of course you need to actively __POE__ all other answer choices, but that's easily done: they are ordered in descending order. And the next answer choice, $$\frac{12}{5}= 2.4$$ is already smaller than 3.
Incorrect. [[Snippet]] When you look at the inequality $$ \frac{1}{x-3} > \frac{5}{8}$$ which of the following is true?
Incorrect.
Correct
Since $$\frac{5}{8}$$ is positive, $$\frac{1}{x-3}$$ is greater than a positive number, which means $$\frac{1}{x-3}$$ itself has to be positive. Thus, $$x-3$$ itself must be positive, which means that $$x > 3$$. So you looked at the expression and determined that $$x$$ has to be more than 3. Now you don't know if it's 3.5 or 58 or any other number, but you do know for sure that any answer that claims $$x$$ is smaller than 3 should be eliminated. Now go back and look at all the answer choices.
$$\frac{16}{5}$$
$$\frac{12}{5}$$
$$2$$
$$\frac{8}{9}$$
$$\frac{4}{5}$$
$$ \frac{1}{x-3}$$ must be positive.
$$ \frac{1}{x-3}$$ must be negative.
$$ \frac{1}{x-3}$$ can be positive or negative.