Hello, Eraser147!
When dealing with inequalities like this: .$\displaystyle |x+4| \:<\:\tfrac{1}{200}$
The problem states that I need to write the given set as an interval or a union of two intervals.
Are both these answers correct?
. . $\displaystyle \left(-\tfrac{801}{200},\,-\tfrac{799}{200}\right)$ . . . . $\displaystyle \left(-\infty,\,-\tfrac{801}{200}\right) \:\cup\:\left(-\tfrac{799}{200},\,\infty\right)$
Obviously, both of them cannot be correct.
Here is helpful rule.
We have an inequality with an absolute value.
If the inequality is "less than", $\displaystyle |x| \:{\color{red}{<}}\: a$
. . then $\displaystyle x$ is between $\displaystyle \text{-}a$ and $\displaystyle +a$.
This is written: .$\displaystyle \text{-}a \,<\,x\,<\,a$
If the inequality is "greater than", $\displaystyle |x|\:{\color{red}{>}}\:a$
. . then $\displaystyle x$ is "outside" of $\displaystyle \text{-}a$ and $\displaystyle +a$.
This is written: .$\displaystyle x\,<\,\text{-}a\;\cup\;x\,>\,a$