## R00nnYBraiNsbiG 2 years ago -3|x-2|+10=12 x = 1 and x = 5 x = −1 and x = −5 x = −9 and x = 3 No Solution

1. R00nnYBraiNsbiG

@AravindG HELP ME PLEASE STEP BY STEP

2. electrokid

$-3|x-2|=2$ now we square this.. the only way to get rid of the absoute sign is to square it

3. electrokid

or make two equations out of it.

4. R00nnYBraiNsbiG

ok wait spuare the hole thing

5. electrokid

yes see the above simplified orm

6. electrokid

$\left[-3|x-2|\right]^2=2^2$

7. R00nnYBraiNsbiG

ok wat about the + 10

8. electrokid

I subtracted it from the two sides

9. electrokid

notice that the right side became 12-10=2

10. R00nnYBraiNsbiG

where did u get the 12 frm

11. R00nnYBraiNsbiG

@electrokid

12. R00nnYBraiNsbiG

where did u get the 12 from

13. electrokid

$-3|x-2|+10=12\qquad\text{....given}\\ \qquad\qquad-10\quad-10$

14. R00nnYBraiNsbiG

ok srry im just learning this ok and then gives u this [−3|x−2|]^2=2^2

15. electrokid

that is ok. well, this first gives $-3|x-2|=2$ so, we the square it like you just wrote above

16. R00nnYBraiNsbiG

yes

17. electrokid

$(-3)^2(x-2)^2=(2^2)$ notice that the absolute sign has disappeared

18. R00nnYBraiNsbiG

so 9*2x-4=4

19. electrokid

or to avoid squaring, you can remove the abolute sign in two ways...... $-3|x-2|=2\implies|x-2|=-{3\over2}$

20. R00nnYBraiNsbiG

how did u get 3/2

21. electrokid

my bad... $\Large{|x-2|=\color{red}{-}{2\over3}}$

22. R00nnYBraiNsbiG

ooh its ok but how did u get that

23. electrokid

divide the two sides by "3"

24. R00nnYBraiNsbiG

ok

25. electrokid

${-3|x-2|\over-3}={2\over-3}$

26. electrokid

this gives the above form.. now, by definition of ABSOLUTE value, can it ever become negative?

27. R00nnYBraiNsbiG

HEY STOP STOP STOP I WROTE THE PROBLEM DWN WRONG SRRY THIS IS THE PROBLEM −3|2x + 6| = −12

28. electrokid

ok... you mean no "10" in there?

29. R00nnYBraiNsbiG

yea

30. electrokid

this is so much different than what you first asked for

31. electrokid

ok.. proceeding similarly, get the absolute quantity on its own...

32. R00nnYBraiNsbiG

ik b/c its 2 differnt problems in one

33. electrokid

$\Large{-3|2x-6|=-12\\\text{divide both sides by -3}\\ |2x-6|=4\\\text{to get rid of absolute sign, we get two possible answers}\\\;\\ 2x-6=4\qquad{\rm AND}\qquad2x-6=-4\\ 2x=4+6\qquad\qquad\qquad2x=-4+6\\ 2x=10\qquad\qquad\qquad\quad2x=2\\ \boxed{x=5}\qquad\qquad\qquad\quad\boxed{x=1}}$

34. electrokid

check, plug in "x=" those numbers in the given problem on the left side. That should give you the right side.

35. R00nnYBraiNsbiG

thanks

36. electrokid

did you understand?

37. R00nnYBraiNsbiG

yes