Geometry

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M is the midpoint of LM
LM=3x+5
LN=5x+40
Find MN

I've tried to work this out several times and am pretty sure I start it off by 3x+5=5(x)+40 but I keep getting a negative answer or a fraction for X and know that is not right. Can someone please help me?

  • Geometry -

    Nope. LM cannot be the midpoint of LM.

    If N is the midpoint of LM, then
    LN is half of LM, so

    3x+5 = 2(5x+40)
    3x+5 = 10x + 80
    7x = -75
    that makes the lengths negative. So, we must have M is the midpoint of LN. In that case,

    5x+40 = 2(3x+5)
    5x+40 = 6x + 10
    x = 30
    So, LM=MN=95
    and LN = 190

  • Geometry -

    L is the midpoint then.
    (3x+5)=(5x+40)
    subtract 3x on both sides.
    5=2x+40
    subtract 40 on both sides.
    -35=2x
    divide by 2.
    -17.5=x
    so yes, it does come out to be negative and a decimal.

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