# solve absolute value inequality with two absolute values

• Sep 7th 2011, 05:56 AM
deathmate
solve absolute value inequality with two absolute values
|3-2x|>|4-x|
->and please someone explain if we can solve inequalities the same way ,for < ,and for > sign?? thanks!
• Sep 7th 2011, 06:11 AM
Plato
Re: solve absolute value inequality with two absolute values
Quote:

Originally Posted by deathmate
|3-2x|>|4-x|
->and please someone explain if we can solve inequalities the same way ,for < ,and for > sign?? thanks!

Do you understand that $|2x-3|>|x-4|$ is the same problem?
Recall that $|a-b|=|b-a|$ because that is just the distance between a & b.

This is true: $|a|\ge |b|\text{ if and only if }a^2\ge b^2.$

So solve $(2x-3)^2>(x-4)^2$. Be sure to check the answers on the original.
• Sep 7th 2011, 07:11 AM
deathmate
Re: solve absolute value inequality with two absolute values
Quote:

Originally Posted by Plato
Do you understand that $|2x-3|>|x-4|$ is the same problem?
Recall that $|a-b|=|b-a|$ because that is just the distance between a & b.

This is true: $|a|\ge |b|\text{ if and only if }a^2\ge b^2.$

So solve $(2x-3)^2>(x-4)^2$. Be sure to check the answers on the original.

thank you so much .> I learned 2 things that I didnt know// I appreciate