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    Given |x-2| + |x-1|>1, how do I find the values of x that satisfy this equation? I know the normal way of solving this is to square both sides, but that doesn't seem to work in this case. Thank you!
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    Draw a graph of y = |x - 2| and y = 1 - |x - 1|
    That should make it easier.
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    (Original post by morgan8002)
    Draw a graph of y = |x - 2| and y = 1 - |x - 1|
    That should make it easier.
    Okay, so it looks like it only holds for x<1 and x>1, but how do I prove this algebraically?
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    (Original post by thescottie)
    Okay, so it looks like it only holds for x<1 and x>1, but how do I prove this algebraically?
    When x<2, |x - 2| = 2 - x
    When x>2, |x - 2| = x - 2


    When x < 1, 1 - |x - 1| = 1 - (1 - x)
    When x > 1, 1 - |x - 1| = 1 - (x - 1)

    Use this information and the graph to find the points of intersection. Then use the graph to find the sign of each critical region.
 
 
 
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