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Math Help - Inequality with absolute values

  1. #1
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    Inequality with absolute values

    hi guys,

    how do you solve this inequality ?

    |x| + |x-1| < 5

    thank you
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  2. #2
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    You probably need to use the Triangle Inequality.

    \displaystyle |a + b| \leq |a| + |b|.


    So that means \displaystyle |x + x - 1| \leq |x| + |x - 1|

    \displaystyle |2x - 1| \leq |x| + |x - 1|.

    And since \displaystyle |x| + |x - 1| < 5 that means

    \displaystyle |2x - 1| < 5.


    Can you go from here?
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  3. #3
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    yeah, cheers !
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  4. #4
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    I was doing a similar question. What is the solution set of mod(2x+5) <= mod(x+1) ? I think it is {x: x=-2, x=4}. The question actually asks for the interval and gives the answer [-4,-2].
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  5. #5
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    The answer is correct. Both sides of the equation can be squared to find the soloution. I have done it now.
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