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Inequality with Modulus sign

I can solve standard types such as

∣5x−3∣<3| 5x - 3 | < 3 as 0<x<65 0 < x < \frac{6}{5}

but what happens when you need to solve something like

3∣x∣+4=6−2∣x∣ 3| x | + 4 = 6 - 2| x |?
Reply 1
Avatar for nuodai
nuodai
17
If you rearrange it then you get 5∣x∣=25|x| = 2, and then you have to solve it under the conditions x<0, x>0x < 0,\ x > 0. It's better to use the different conditions than it is to square it, especially if it's an inequality.
Reply 2
Avatar for Bluebird92
Bluebird92
OP
8
nuodai
If you rearrange it then you get 5∣x∣=25|x| = 2, and then you have to solve it under the conditions x<0, x>0x < 0,\ x > 0. It's better to use the different conditions than it is to square it, especially if it's an inequality.


It looks easier than I thought it would be :smile:

So the solution surely would be −25<x<25-\frac{2}{5} < x < \frac{2}{5} ?
Reply 3
Avatar for nuodai
nuodai
17
Bluebird92
It looks easier than I thought it would be :smile:

So the solution surely would be −25<x<25-\frac{2}{5} < x < \frac{2}{5} ?

Yup :smile:

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