## anonymous one year ago solve for x: −3|2x + 6| = −12 a. x = −1 and x = −5 <--- correct answer b. no solution c. x = 1 and x = 5 d. x = −9 and x = 3

1. jim_thompson5910

|dw:1434963289424:dw|

2. jim_thompson5910

first you can divide both sides by -3 |dw:1434963323427:dw|

3. jim_thompson5910

|dw:1434963334417:dw|

4. jim_thompson5910

|dw:1434963344378:dw|

5. jim_thompson5910

make sense so far?

6. anonymous

yes, wow thank you. i kept distributing

7. jim_thompson5910

so you will have |2x+6| = 4

8. jim_thompson5910

|2x+6| = 4 breaks down into these two equations 2x+6 = 4 or 2x+6 = -4

9. UsukiDoll

does the absolute value rule also apply here?

10. UsukiDoll

I thought.. it's 2x+6=4 or -2x-6= 4...or am I remembering this wrong?

11. jim_thompson5910

either way works because -2x-6 = 4 is equivalent to 2x+6 = -4

12. UsukiDoll

oh ok! I prefer either we have 2x+6 =4 or -2x-6=4 whew

13. UsukiDoll

so now all we need to do is solve for x for those equations.

14. anonymous

i got -5 twice???

15. UsukiDoll

oh there it is! For an absolute value equation, we split this equation into 2 situations. one where $\abs 2x+6 \abs = 4$ Y U NO WORK LATEX NUGH! we have one situation where the 2x+6 is positive and another situation is the negative sign is distributed all over 2x+6

16. UsukiDoll

2x+ 6 = 4 -2x-6=4 should be our equations

17. UsukiDoll

let's start at 2x+6=4 solve for x

18. anonymous

x = 5

19. anonymous

x = -5 sorry

20. UsukiDoll

if x = -5 and I plug it back into the equation I have -4.. -4 doesn't equal to 4 for 2x+6=4

21. UsukiDoll

I need x by itself.. so what do we need to do?

22. anonymous

subtract 6 on both sides, then divide by 2

23. UsukiDoll

yeah

24. UsukiDoll

$2x+6=4$ $2x=4-6$ $2x=-2$

25. anonymous

ohhh ok so x = -1

26. UsukiDoll

right so our next equation -2x-6=4

27. UsukiDoll

so what do we need to do to get x by itself ^^

28. UsukiDoll

@jillybean367 are you there? ^^

29. anonymous

add 6 to both sides, then multiply by 2?

30. UsukiDoll

yes for addition part, but no for the multiplication $-2x-6=4$ $-2x-6+6=4+6$ $-2x=10$

31. anonymous

divide by -2

32. UsukiDoll

mhm and what do we have?

33. anonymous

x =5 ?

34. UsukiDoll

close you are dividing a positive number with a negative number example $\frac{-12}{4} = -3$

35. UsukiDoll

so in your problem we have $x = \frac{10}{-2}$ or $x = \frac{-10}{2}$

36. UsukiDoll

what is x?

37. anonymous

5?

38. UsukiDoll

the answer has a negative sign though...

39. UsukiDoll

we can't drop the negative sign.

40. anonymous

oh. so its x = -5?

41. UsukiDoll

yes, so we have x = -1 and x = -5 if you plug those values back in the original equation you will have -12=-12 so those are the correct x values

42. anonymous

Wow thank you so much!