anonymous
  • anonymous
I'm trying to do an absolute value equation. |4x – 5| – 3x = 2x + 9 I have already solved the positive case of the solution and got -14. But I'm struggling with the negative case: 4x – 5 = -5x - 9 (is THAT even right?) It seems like no matter what I do, none of the numbers I come up with fit. Is this an example of an extraneous solution, or can someone help me find x's value?
Mathematics
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anonymous
  • anonymous
I'm trying to do an absolute value equation. |4x – 5| – 3x = 2x + 9 I have already solved the positive case of the solution and got -14. But I'm struggling with the negative case: 4x – 5 = -5x - 9 (is THAT even right?) It seems like no matter what I do, none of the numbers I come up with fit. Is this an example of an extraneous solution, or can someone help me find x's value?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Tried to do it again by setting it up to equal 0. Can anyone confirm this? 4x – 5 = -5x – 9 4x – 5 – (-5x -9) = 0 9x + 4 = 0 Subtract 4: 9x = -4 Divide by 9: x =-4/9
LynFran
  • LynFran
\[|4x-5|-3x=2x+9\]\[|4x-5|-3x+3x=2x+3x+9\]\[|4x-5|=(5x+9)\]\[(4x-5)=\pm (5x+9)\]equation 1\[4x-5=5x+9\]and equation 2 \[4x-5=-(5x+9)\]
LynFran
  • LynFran
for equation 1 we get \[4x-5=5x+9\]\[-5-9=5x-4x\]\[-14=x\]

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LynFran
  • LynFran
for equation 2 we get \[4x-5=-(5x+9)\]\[4x-5=-5x-9\]\[-5+9=-5x-4x\]\[4=-9x\]\[\frac{ -4 }{ 9 }=x\]
anonymous
  • anonymous
Thank you! :)
LynFran
  • LynFran
welcome

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