anonymous 3 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. anonymous

@AravindG HELP ME PLEASE STEP BY STEP

2. anonymous

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

3. anonymous

or make two equations out of it.

4. anonymous

ok wait spuare the hole thing

5. anonymous

yes see the above simplified orm

6. anonymous

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

7. anonymous

ok wat about the + 10

8. anonymous

I subtracted it from the two sides

9. anonymous

notice that the right side became 12-10=2

10. anonymous

where did u get the 12 frm

11. anonymous

@electrokid

12. anonymous

where did u get the 12 from

13. anonymous

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

14. anonymous

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

15. anonymous

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

16. anonymous

yes

17. anonymous

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

18. anonymous

so 9*2x-4=4

19. anonymous

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

20. anonymous

how did u get 3/2

21. anonymous

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

22. anonymous

ooh its ok but how did u get that

23. anonymous

divide the two sides by "3"

24. anonymous

ok

25. anonymous

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

26. anonymous

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

27. anonymous

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

28. anonymous

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

29. anonymous

yea

30. anonymous

this is so much different than what you first asked for

31. anonymous

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

32. anonymous

ik b/c its 2 differnt problems in one

33. anonymous

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

34. anonymous

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

35. anonymous

thanks

36. anonymous

did you understand?

37. anonymous

yes