What is the difference between... these two intervals

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When dealing with inequalities like this Attachment 25088, Attachment 25089 The problem states that I need to write the given set as an interval or a union of two intervals. Are the answers above both correct? Click image to enlarge please.

Re: What is the difference between... these two intervals

Hello, Eraser147!

Quote:

When dealing with inequalities like this: . $|x+4| \:<\:\tfrac{1}{200}$

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?

. . $\left(-\tfrac{801}{200},\,-\tfrac{799}{200}\right)$ . . . . $\left(-\infty,\,-\tfrac{801}{200}\right) \:\cup\:\left(-\tfrac{799}{200},\,\infty\right)$

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", $|x| \:{\color{red}{<}}\: a$
. . then $x$ is between $\text{-}a$ and $+a$ .
This is written: . $\text{-}a \,<\,x\,<\,a$

If the inequality is "greater than", $|x|\:{\color{red}{>}}\:a$
. . then $x$ is "outside" of $\text{-}a$ and $+a$ .
This is written: . $x\,<\,\text{-}a\;\cup\;x\,>\,a$

Re: What is the difference between... these two intervals

Very helpful, thank you very much.