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.

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- Oct 6th 2012, 07:18 PMEraser147What is the difference between... these two intervals
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.

- Oct 6th 2012, 08:08 PMSorobanRe: What is the difference between... these two intervals
Hello, Eraser147!

Quote:

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$\displaystyle \text{-}a$ and $\displaystyle +a$.*between*

This is written: .$\displaystyle \text{-}a \,<\,x\,<\,a$

If the inequality is "greater than", $\displaystyle |x|\:{\color{red}{>}}\:a$

. . then $\displaystyle x$ is "" of $\displaystyle \text{-}a$ and $\displaystyle +a$.*outside*

This is written: .$\displaystyle x\,<\,\text{-}a\;\cup\;x\,>\,a$

- Oct 6th 2012, 08:28 PMEraser147Re: What is the difference between... these two intervals
Very helpful, thank you very much.