Question: Absolute Inequality Starring p

Comment on Absolute Inequality Starring p

In the explanation, why did -p/2 become p/-2?

Thanks to hear,

Kind regards,
greenlight-admin's picture

Hi Ryan,
Those expressions are equivalent, in the same way that (-6)/2 = 6/(-2).
Both are equal to -3
Does that help?

Can I understand that this is trying to have the variable p as a positive value?
greenlight-admin's picture

Our goal is to find possible values of p, not -p
This is why I rewrote the expression in terms of p

Now I get it, Thanks.

Instead of first dividing all sides by 3, I multiplied it to show -15<((-3p/2)-3)<15. After carrying out the operations, I got: -9<p<8, which is incorrect. How do I know that I must divide by the 3 before the operations?
greenlight-admin's picture

I'd be careful to avoid rewriting 3|-p/2 - 1| as |-3p/2 - 3|, since this COULD lead to errors with other questions.

However, taking from -15 < ((-3p/2)-3) < 15, we can still arrive at the correct solution.

You have: -15 < -3p/2 - 3 < 15
Add 3 to all sides: -12 < -3p/2 < 18
Multiply all sides by 2: -24 < -3p < 36
Divide all sides by -3: 8 > p > -12
Rewrite as: -12 < p < 8

This is the same conclusion as in the video solution.


Hello Brent.
why did not you perform the negative value of |-p/2 - 1|
absolute value of |x| can be +x and -x.

greenlight-admin's picture

Hi Aziz.

The solution does consider the negative value of |-p/2 - 1|

Once we know that: |-p/2 - 1| < 5
We rewrite it as: -5 < -p/2 - 1 < 5
As you can see, the -5 here takes care of the negative value of -p/2 - 1

Does that help?

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