## anonymous one year ago Solve for x. -ax + 3b > 5 x > the quantity 3 times b minus 5 all over negative a x > the quantity 5 minus 3 times b all over negative a x < the quantity 3 times b plus 5 all over negative a x < the quantity negative 3 times b plus 5 all over negative a

1. anonymous

@nincompoop

2. dan815

okay so if you were to subtract the same quantitity from both sides the inequality still holds

3. dan815

for example| say we have 5>4 which is true if we subtract 2 from both sides 5-2>4-2 we just shifted the numbers down by 2 3>2

4. dan815

same thing with multiplication

5. dan815

suppose a > b then 3a>3b is still true

6. dan815

|dw:1435216228375:dw|

7. anonymous

subtract 3 from each side?

8. anonymous

nvm

9. dan815

the final rule you need to know is

10. dan815

multiplication by -1 or any negative number, here is where the inequality flips

11. dan815

if a > b then -a < -b

12. dan815

this can be seen more clearly with number line examples

13. dan815

|dw:1435216365389:dw|

14. dan815

|dw:1435216407582:dw|

15. dan815

the distance from the 0 is the same, however now a is MORE negative and b is LESS negative

16. dan815

so -a<-b and a>b

17. dan815

ill leave you with an excercise show this is still true, when a is negative and b is positive to start with

18. dan815

lool

19. dan815

that guy called us nerds and left

20. dan815

arent u enraged

21. Astrophysics

lol

22. Astrophysics

slow down dan

23. anonymous

im just so confused

24. Astrophysics

thats what dan does he throws bunch of info at you and expects you to get it, he's a noobie, im the hero I'll save you

25. Astrophysics

lolol

26. dan815

make sure u read all that over! after astros help

27. dan815

28. anonymous

you lost me at "if a > b then -a < -b"

29. dan815

imagine the number line,

30. anonymous

yeah that number line got me confused lol

31. Astrophysics

I think you should do the algebra first and then you can figure it out

32. Astrophysics

Dan gave lots of good info, but he's a hyper one and a smart one :P, so lets take it down a bit.

33. anonymous

34. Astrophysics

|dw:1435216787284:dw| so this is what we're given right and we need to solve for x, so a rule I'll say right now, when we do algebra with inequalities, if we multiply OR divide by a negative number the sign of the inequality flips ok?

35. anonymous

ok

36. Astrophysics

Great, so lets start off and do our algebra, any idea what we can do with 3b?

37. anonymous

divide it with 3?

38. Astrophysics

Well, we want to move everything but the x on the left side, meaning we isolate x/ solving x. So to do this an easy way to look at it is, do the opposite of what operation already exists, so notice we have +3b to cancel it out (we want 0 3b's on the left) we would subtract it, as follow: |dw:1435217000808:dw| and remember what we do to one side we MUST also do it to the other.

39. Astrophysics

That should say to the right side sorry* :P

40. Astrophysics

|dw:1435217056160:dw| so now we have this, let me know when you're ready to move on

41. anonymous

ok got it

42. Astrophysics

Alright cool, so what should we do next, remember we want to keep x there, but not the -a, but we can't have -a be 0 otherwise x will be 0 to and it would make no sense!

43. Astrophysics

What operation do you think would be best :)

44. anonymous

get rid of the -a by adding a?

45. Astrophysics

Nice try, but notice it's "attached" to the x, that means it's being multiplied, so we divide by -a on both sides!

46. Astrophysics

Also remember the little rule I mentioned earlier, what happens if we divide by a negative sign?

47. anonymous

it becomes a positive?

48. Astrophysics

I mean to the inequality

49. Astrophysics

|dw:1435217372626:dw| remember the sign flips

50. anonymous

51. Astrophysics

|dw:1435217417366:dw| now we can put it in words, I will let you figure that out!

52. Astrophysics

But everything so far makes sense right?

53. anonymous

so far yes

54. Astrophysics

Ok so try comparing it with one of your options and see if you can get it

55. Astrophysics

Or you can leave the answer as |dw:1435217588112:dw|

56. anonymous

option A?

57. Astrophysics

Mhm, is it x< or is it x>

58. Astrophysics

You be able to eliminate two answers right away

59. anonymous

>

60. Astrophysics

Lol just look at the answer

61. Astrophysics

It's right there!

62. anonymous

it doesnt show the same answer for the options

63. Astrophysics

|dw:1435217852979:dw|

64. anonymous

65. anonymous

3b+5/a?

66. Astrophysics

$$\color{blue}{\text{Originally Posted by}}$$ @CatalystDuzIt Solve for x. -ax + 3b > 5 x > the quantity 3 times b minus 5 all over negative a x > the quantity 5 minus 3 times b all over negative a x < the quantity 3 times b plus 5 all over negative a x < the quantity negative 3 times b plus 5 all over negative a $$\color{blue}{\text{End of Quote}}$$ We can eliminate the first one and the second option, so look at three and four.

67. Astrophysics

I think this will make it clear |dw:1435217982712:dw|

68. Astrophysics

|dw:1435218006866:dw|

69. anonymous

yeah thats it

70. anonymous

thanks man. i appreciate it!

71. Astrophysics

No worries, the answers they gave you are in a way you would never put...so yeah haha.