# Thread: solve absolute value inequality with two absolute values

1. ## 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!

2. ## Re: solve absolute value inequality with two absolute values

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

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

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

3. ## Re: solve absolute value inequality with two absolute values

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

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

So solve $\displaystyle (2x-3)^2>(x-4)^2$. Be sure to check the answers on the original.
thank you so much .> I learned 2 things that I didnt know// I appreciate