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Math Help - solve absolute value inequality with two absolute values

  1. #1
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    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!
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  2. #2
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    Re: solve absolute value inequality with two absolute values

    Quote Originally Posted by deathmate View Post
    |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.
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  3. #3
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    Re: solve absolute value inequality with two absolute values

    Quote Originally Posted by Plato View Post
    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
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