|3-2x|>|4-x|

->and please someone explain if we can solve inequalities the same way ,for < ,and for > sign?? thanks!

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- Sep 7th 2011, 05:56 AMdeathmatesolve 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 AMPlatoRe: solve absolute value inequality with two absolute values
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. - Sep 7th 2011, 07:11 AMdeathmateRe: solve absolute value inequality with two absolute values