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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

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  1. anonymous
    • one year ago
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    @nincompoop

  2. dan815
    • one year ago
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    okay so if you were to subtract the same quantitity from both sides the inequality still holds

  3. dan815
    • one year ago
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    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
    • one year ago
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    same thing with multiplication

  5. dan815
    • one year ago
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    suppose a > b then 3a>3b is still true

  6. dan815
    • one year ago
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    |dw:1435216228375:dw|

  7. anonymous
    • one year ago
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    subtract 3 from each side?

  8. anonymous
    • one year ago
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    nvm

  9. dan815
    • one year ago
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    the final rule you need to know is

  10. dan815
    • one year ago
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    multiplication by -1 or any negative number, here is where the inequality flips

  11. dan815
    • one year ago
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    if a > b then -a < -b

  12. dan815
    • one year ago
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    this can be seen more clearly with number line examples

  13. dan815
    • one year ago
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    |dw:1435216365389:dw|

  14. dan815
    • one year ago
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    |dw:1435216407582:dw|

  15. dan815
    • one year ago
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    the distance from the 0 is the same, however now a is MORE negative and b is LESS negative

  16. dan815
    • one year ago
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    so -a<-b and a>b

  17. dan815
    • one year ago
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    ill leave you with an excercise show this is still true, when a is negative and b is positive to start with

  18. dan815
    • one year ago
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    lool

  19. dan815
    • one year ago
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    that guy called us nerds and left

  20. dan815
    • one year ago
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    arent u enraged

  21. Astrophysics
    • one year ago
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    lol

  22. Astrophysics
    • one year ago
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    slow down dan

  23. anonymous
    • one year ago
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    im just so confused

  24. Astrophysics
    • one year ago
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    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
    • one year ago
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    lolol

  26. dan815
    • one year ago
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    make sure u read all that over! after astros help

  27. dan815
    • one year ago
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    its important, please do it

  28. anonymous
    • one year ago
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    you lost me at "if a > b then -a < -b"

  29. dan815
    • one year ago
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    imagine the number line,

  30. anonymous
    • one year ago
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    yeah that number line got me confused lol

  31. Astrophysics
    • one year ago
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    I think you should do the algebra first and then you can figure it out

  32. Astrophysics
    • one year ago
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    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
    • one year ago
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    please lol

  34. Astrophysics
    • one year ago
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    |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
    • one year ago
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    ok

  36. Astrophysics
    • one year ago
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    Great, so lets start off and do our algebra, any idea what we can do with 3b?

  37. anonymous
    • one year ago
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    divide it with 3?

  38. Astrophysics
    • one year ago
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    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
    • one year ago
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    That should say to the right side sorry* :P

  40. Astrophysics
    • one year ago
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    |dw:1435217056160:dw| so now we have this, let me know when you're ready to move on

  41. anonymous
    • one year ago
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    ok got it

  42. Astrophysics
    • one year ago
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    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
    • one year ago
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    What operation do you think would be best :)

  44. anonymous
    • one year ago
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    get rid of the -a by adding a?

  45. Astrophysics
    • one year ago
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    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
    • one year ago
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    Also remember the little rule I mentioned earlier, what happens if we divide by a negative sign?

  47. anonymous
    • one year ago
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    it becomes a positive?

  48. Astrophysics
    • one year ago
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    I mean to the inequality

  49. Astrophysics
    • one year ago
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    |dw:1435217372626:dw| remember the sign flips

  50. anonymous
    • one year ago
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    oh yeah my bad

  51. Astrophysics
    • one year ago
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    |dw:1435217417366:dw| now we can put it in words, I will let you figure that out!

  52. Astrophysics
    • one year ago
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    But everything so far makes sense right?

  53. anonymous
    • one year ago
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    so far yes

  54. Astrophysics
    • one year ago
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    Ok so try comparing it with one of your options and see if you can get it

  55. Astrophysics
    • one year ago
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    Or you can leave the answer as |dw:1435217588112:dw|

  56. anonymous
    • one year ago
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    option A?

  57. Astrophysics
    • one year ago
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    Mhm, is it x< or is it x>

  58. Astrophysics
    • one year ago
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    You be able to eliminate two answers right away

  59. anonymous
    • one year ago
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    >

  60. Astrophysics
    • one year ago
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    Lol just look at the answer

  61. Astrophysics
    • one year ago
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    It's right there!

  62. anonymous
    • one year ago
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    it doesnt show the same answer for the options

  63. Astrophysics
    • one year ago
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    |dw:1435217852979:dw|

  64. anonymous
    • one year ago
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    doesnt show the same answer

  65. anonymous
    • one year ago
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    3b+5/a?

  66. Astrophysics
    • one year ago
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    \(\color{blue}{\text{Originally Posted by}}\) @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
    • one year ago
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    I think this will make it clear |dw:1435217982712:dw|

  68. Astrophysics
    • one year ago
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    |dw:1435218006866:dw|

  69. anonymous
    • one year ago
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    yeah thats it

  70. anonymous
    • one year ago
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    thanks man. i appreciate it!

  71. Astrophysics
    • one year ago
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    No worries, the answers they gave you are in a way you would never put...so yeah haha.

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