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## Ibbutibbu. one year ago Can someone plx help me? -|3x + 4| = 5x + 4

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1. DecentNabeel

$-\left|3x+4\right|=5x+4\quad :\quad x=-1$

2. 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

3. Ibbutibbu.

so one is 2x = 0?

4. Ibbutibbu.

and one is x=1?

5. Ibbutibbu.

i think the 1st oneis wrong

6. DecentNabeel

@Ibbutibbu. i am right x=-1

7. freckles

one solution you will see not work out because both sides will not be the same

8. freckles

@DecentNabeel he might want to know how to get the solution

9. Ibbutibbu.

yeah ^^^

10. 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

11. freckles

but plugging them into the original equation

12. freckles

$-|3x+4|=5x+4 \\ \text{ for example are both of these true: } \\ -|3(-1)+4|=5(-1)+4 \\ -|3(0)+4|=5(0)+4$

13. freckles

if not which is true

14. Ibbutibbu.

i think they are both correct

15. 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

16. 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

17. DecentNabeel

are you understand @freckles

18. freckles

what does that means "are you understand @freckles "

19. DecentNabeel

nothing mean :)

20. 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

21. Ibbutibbu.

well, this is getting interesting

22. freckles

oops 0 wasn't less than or equal to -4/5*

23. freckles

but I think what you meant to ask me earlier @DecentNabeel was "do you understand @freckles "

24. Ibbutibbu.

i have one question |7x - 5| are the two things 7x + 5 and -7x - 5 ???

25. 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

26. Ibbutibbu.

ok thx

27. Ibbutibbu.

ima close it now

28. DecentNabeel

i said x=-1 is the solution.. but you said that are not correct.. then finally you are agree with me :)

29. Ibbutibbu.

u guys have been awesome

30. freckles

I never disagreed with you @DecentNabeel

31. freckles

@DecentNabeel where above did I ever say x=-1 wasn't the solution

32. DecentNabeel

ok:)

33. freckles

@DecentNabeel I think you should reread the conversation above because you might have gotten lost somewhere along the way.

34. DecentNabeel

yes i cannot read the conversation above.. continue @freckles

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