Question

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?

Answer 1

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

Answer 2

\[|4x-5|-3x=2x+9\]\[|4x-5|-3x+3x=2x+3x+9\]\[|4x-5|=(5x+9)\]\[(4x-5)=\pm (5x+9)\]equation 1\[4x-5=5x+9\]and equation 2 \[4x-5=-(5x+9)\]

Answer 3

for equation 1 we get \[4x-5=5x+9\]\[-5-9=5x-4x\]\[-14=x\]

Answer 4

for equation 2 we get \[4x-5=-(5x+9)\]\[4x-5=-5x-9\]\[-5+9=-5x-4x\]\[4=-9x\]\[\frac{ -4 }{ 9 }=x\]

Answer 5

Thank you! :)

Answer 6

welcome