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anonymous

  • one year ago

I need help! 12x-5/12 + 3-x/4 < 4/3 *** supposed to be a less than or equal to, but I don't have that sign.

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  1. phi
    • one year ago
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    you can use <= or less than or equal

  2. anonymous
    • one year ago
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    Okay

  3. phi
    • one year ago
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    is it \[ \frac{12x-5}{12} + \frac{3-x}{4} \le \frac{4}{3} \] ? I would multiply both sides by 12 (that means *every* term on both sides) as a first step. can you do that ?

  4. anonymous
    • one year ago
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    Yes that's correct

  5. anonymous
    • one year ago
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    So like distribute a 12 in?

  6. phi
    • one year ago
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    yes, but on both sides

  7. anonymous
    • one year ago
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    12x-5+3 (3-x) <= 16?

  8. phi
    • one year ago
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    yes, now distribute the 3

  9. anonymous
    • one year ago
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    12x-5+9-3x <=16

  10. phi
    • one year ago
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    now combine "like terms"

  11. phi
    • one year ago
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    12 x's take away 3 x's and -5+9

  12. anonymous
    • one year ago
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    9x+4 <=16

  13. phi
    • one year ago
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    now add -4 to both sides

  14. anonymous
    • one year ago
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    9x <=12?

  15. phi
    • one year ago
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    yes. now divide both sides by 9 (remember it's ok to divide by positive numbers)

  16. anonymous
    • one year ago
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    Ok

  17. phi
    • one year ago
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    \[ \frac{9x}{9} \le \frac{12}{9} \] and 9/9 on the left side simplifies to 1

  18. phi
    • one year ago
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    and we can simplify 12/9 (divide top and bottom by 3)

  19. anonymous
    • one year ago
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    Uhm but I think the answer is supposed to be x greater than or equal to -12

  20. phi
    • one year ago
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    Are you sure we started with the correct problem? for the problem I posted we get x <= 4/3

  21. anonymous
    • one year ago
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    Yes

  22. anonymous
    • one year ago
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    I'm confused hsha

  23. phi
    • one year ago
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    if the answer is really x>= -12 then x= 2 should work (but won't because we know x<= 4/3 (1 and 1/3) ) using x=2 in the problem \[ \frac{12x-5}{12} + \frac{3-x}{4} \le \frac{4}{3} \\ \frac{24-5}{12} + \frac{3-2}{4} \le \frac{4}{3} \\ \frac{19}{12} +\frac{3}{12} \le \frac{4}{3} \\ \frac{22}{12} \le \frac{4}{3} \\ 1.833... \le 1.333... \] which is not true (as we know)

  24. phi
    • one year ago
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    Here are the possible problems: 1) typo in the problem 2) typo in answer key

  25. anonymous
    • one year ago
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    Wait... it's actually a problem that some one did and I have to explain where they went wrong

  26. phi
    • one year ago
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    maybe if you post a copy of the page...

  27. phi
    • one year ago
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    take a screen shot or a picture

  28. anonymous
    • one year ago
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    How do I post the picture tho?

  29. phi
    • one year ago
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    click on "attach file"

  30. anonymous
    • one year ago
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    It doesn't say that for me

  31. phi
    • one year ago
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    are you at a computer or using the iPad app?

  32. anonymous
    • one year ago
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    I'm on my phone

  33. phi
    • one year ago
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    do you see a paper clip icon ?

  34. anonymous
    • one year ago
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    just got on laptop gimme a sec

  35. anonymous
    • one year ago
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  36. phi
    • one year ago
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    do you see what they did wrong?

  37. anonymous
    • one year ago
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    they didnt change the 4/3?

  38. phi
    • one year ago
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    yes. as for *our problem* we started with (12x-5)/12 and it should be (2x-5)/12

  39. anonymous
    • one year ago
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    oh. orry

  40. anonymous
    • one year ago
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    sorry*

  41. phi
    • one year ago
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    of course that changes everything.

  42. anonymous
    • one year ago
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    yeah

  43. phi
    • one year ago
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    can you do the work ? this one is more tricky because we will get a negative x

  44. anonymous
    • one year ago
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    let me try

  45. anonymous
    • one year ago
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    im stuck at -x+4<=16

  46. phi
    • one year ago
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    add -4 to both sides

  47. anonymous
    • one year ago
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    i subtract 4 and then divide by -1 right?

  48. anonymous
    • one year ago
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    then the sign flips

  49. phi
    • one year ago
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    with relations, if you divide by a negative number you have to remember to flip the relation once you get to -x <= 12 you can divide by -1 and flip to get x >= -12 or , remember it's always safe to add or subtract. so we could add +x to both sides: -x + x <= 12 + x 0 <= 12 + x now add -12 to both sides -12 <= x which can also be written x>= -12

  50. anonymous
    • one year ago
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    okay :)

  51. anonymous
    • one year ago
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    thanks so much!

  52. phi
    • one year ago
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    yw

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