## anonymous one year ago 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?

1. 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

2. 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 $4x-5=-(5x+9)$

3. LynFran

for equation 1 we get $4x-5=5x+9$$-5-9=5x-4x$$-14=x$

4. LynFran

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

5. anonymous

Thank you! :)

6. LynFran

welcome