Ibbutibbu.
  • Ibbutibbu.
Can someone plx help me? -|3x + 4| = 5x + 4
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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DecentNabeel
  • DecentNabeel
\[-\left|3x+4\right|=5x+4\quad :\quad x=-1\]
freckles
  • freckles
|3x+4|=-(5x+4) anyways you have two equations to solve: 3x+4=-(5x+4) or also 3x+4=5x+4 then check solutions
Ibbutibbu.
  • Ibbutibbu.
so one is 2x = 0?

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Ibbutibbu.
  • Ibbutibbu.
and one is x=1?
Ibbutibbu.
  • Ibbutibbu.
i think the 1st oneis wrong
DecentNabeel
  • DecentNabeel
@Ibbutibbu. i am right x=-1
freckles
  • freckles
one solution you will see not work out because both sides will not be the same
freckles
  • freckles
@DecentNabeel he might want to know how to get the solution
Ibbutibbu.
  • Ibbutibbu.
yeah ^^^
freckles
  • freckles
\[3x+4=-(5x+4) \\ 3x+4=-5x-4 \\ 3x+5x=-4-4 \\ 8x=-8 \\ x=-1 \\ \text{ then also } 3x+4=5x+4 \\ 3x-5x=4-4 \\ -2x=0 \\ x=0 \] we can check both of these to see if they are actually solutions
freckles
  • freckles
but plugging them into the original equation
freckles
  • freckles
\[-|3x+4|=5x+4 \\ \text{ for example are both of these true: } \\ -|3(-1)+4|=5(-1)+4 \\ -|3(0)+4|=5(0)+4\]
freckles
  • freckles
if not which is true
Ibbutibbu.
  • Ibbutibbu.
i think they are both correct
DecentNabeel
  • DecentNabeel
\[3x+4\ge \:0\:\mathrm{for}\:x\ge \:-\frac{4}{3},\:\quad \mathrm{\therefore\:for}\:x\ge \:-\frac{4}{3}\quad \left|3x+4\right|=3x+4\] \[3x+4<0\:\mathrm{for}\:x<-\frac{4}{3},\:\quad \mathrm{\therefore\:for}\:x<-\frac{4}{3}\quad \left|3x+4\right|=-\left(3x+4\right)\] \[\mathrm{Evaluate\:the\:expression\:\in\:the\:following\:ranges:}\] \[x<-\frac{4}{3},\:x\ge \:-\frac{4}{3}\] \[-\left(-\left(3x+4\right)\right)=5x+4\quad :\quad x=0\] \[-\left(3x+4\right)=5x+4\quad :\quad x=-1\] combine the range \[\left(x<-\frac{4}{3}\:\:\:\mathrm{and}\:\:\:\:x=0\right)\:\:\:\mathrm{or}\:\:\:\left(x\ge \:-\frac{4}{3}\:\:\:\mathrm{and}\:\:\:\:x=-1\right)\] x=-1
freckles
  • freckles
well looking at that second equation I wrote: -|3(0)+4|=5(0)+4 -|0+4|=0+4 -|4|=4 -4=4 <--this isn't a true equation so x=0 is definitely not a solution
DecentNabeel
  • DecentNabeel
are you understand @freckles
freckles
  • freckles
what does that means "are you understand @freckles "
DecentNabeel
  • DecentNabeel
nothing mean :)
freckles
  • freckles
well if you don't understand my explanation here is another way to look at it @DecentNabeel \[-|3x+4|=5x+4 \\ |3x+4|=-(5x+4) \\ \text{ we need } 5x+4 \le 0 \\ x \le \frac{-4}{5}\] and x wasn't less than or equal to -4/5 but -1 is so x=-1 is the only solution
Ibbutibbu.
  • Ibbutibbu.
well, this is getting interesting
freckles
  • freckles
oops 0 wasn't less than or equal to -4/5*
freckles
  • freckles
but I think what you meant to ask me earlier @DecentNabeel was "do you understand @freckles "
Ibbutibbu.
  • Ibbutibbu.
i have one question |7x - 5| are the two things 7x + 5 and -7x - 5 ???
freckles
  • freckles
|7x-5| can be 7x-5 or -7x+5 |7x-5| is 7x-5 only when 7x-5>=0 |7x-5| is -(7x-5) only when 7x-5<=0
Ibbutibbu.
  • Ibbutibbu.
ok thx
Ibbutibbu.
  • Ibbutibbu.
ima close it now
DecentNabeel
  • DecentNabeel
i said x=-1 is the solution.. but you said that are not correct.. then finally you are agree with me :)
Ibbutibbu.
  • Ibbutibbu.
u guys have been awesome
freckles
  • freckles
I never disagreed with you @DecentNabeel
freckles
  • freckles
@DecentNabeel where above did I ever say x=-1 wasn't the solution
DecentNabeel
  • DecentNabeel
ok:)
freckles
  • freckles
@DecentNabeel I think you should reread the conversation above because you might have gotten lost somewhere along the way.
DecentNabeel
  • DecentNabeel
yes i cannot read the conversation above.. continue @freckles

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