Evaluating absolute inequalities

Question

I have the *expression $$\frac{1}{\sqrt{4a^2-b^2}}$$

and I am being asked to evaluate the case when $2|a| \geq|b|$

Logically I know what this statement mean but don't know how it applies to this problem: Cases when $a$ is twice greater than the distance of $b$ is from $0$. (Correct me if i'm wrong)

I also know that absolute values on both sides of an equation are inpracticle and it would be better to write the inequality as $|a/b| \geq 1/2$.

Which can also be written as $a/b \geq 1/2$ or $a/b \leq 1/2$ which doesn't make any sense.

here's a link to the problem (#3) https://i.stack.imgur.com/ZdBbK.jpg

Thank you, I would appreciate help I've been struggling with this for a while

Answer 1

we have $$\frac{\sqrt{4a^2-b^2}}{-(4a^2-b^2)}=-\frac{1}{\sqrt{4a^2-b^2}}$$ and here we have $$2|a|>|b|$$

Answer 2

The only reason they say $2|a| \geq|b|$ is that if $2|a| \not\geq|b|$, the square root $\sqrt{4a^2 - b^2}$ doesn't make sense.