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ilovenyc

-7y - 17 > 11 Part 1: Solve the inequality above. Part 2: Describe the graph of the solution.

  • one year ago
  • one year ago

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  1. srossd
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    To solve this, first you have to separate variables and constants. To do that, add 17 to both sides: -7y > 28 Now, isolate the variable by dividing both sides by -7. Remember when you multiply or divide by a negative number, the greater than changes to a less than. So, the solution is: y < -4 The graph of this will be a number line with an open circle on -4, and everything to the left of -4 shaded, like this:|dw:1356664453181:dw|

    • one year ago
  2. ilovenyc
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    @srossd thank you so much! can you help me with another

    • one year ago
  3. srossd
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    Yeah, sure.

    • one year ago
  4. ilovenyc
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    2x + 1 5 or -3x > -9 Part 1: Solve the inequality above. Part 2: Describe the graph of the solution.

    • one year ago
  5. srossd
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    Looks like the symbol didn't print - it was probably >= or <=. Can you tell me which one?

    • one year ago
  6. ilovenyc
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    |dw:1356665051133:dw|

    • one year ago
  7. ilovenyc
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    can you read that?

    • one year ago
  8. srossd
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    Great, thanks. So here's how to simplify them:|dw:1356665108128:dw| Remember, on the second one, the greater than sign switches because I divided by a negative.

    • one year ago
  9. srossd
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    And same to you, tell me if you have trouble reading.

    • one year ago
  10. srossd
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    Here's the graph:|dw:1356665170251:dw| Remember, open circle for plain old less/greater than, closed circle for "or equal to".

    • one year ago
  11. ilovenyc
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    can you write the answer please?

    • one year ago
  12. srossd
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    Yeah, sure. x >= 2 or x < 3. And good thing I did that, turns out I did the graph for "and" - for "or," it's just the whole number line shaded.

    • one year ago
  13. ilovenyc
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    okay and can you write out part 2 please @srossd

    • one year ago
  14. srossd
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    Yeah, it's not much more complicated than what I said: the graph of the two inequalities will be the entire number line shaded, since every number is either >= 2 or < 3.

    • one year ago
  15. ilovenyc
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    @srossd THANKS SO MUCH! can you help me with some more?

    • one year ago
  16. srossd
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    Yeah, definitely.

    • one year ago
  17. ilovenyc
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    @srossd Which of the following inequalities matches the graph? (see attached photo) A y < x + 3 B x + 3 C y x + 3 D The correct inequality is not listed.

    • one year ago
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  18. srossd
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    Well, to graph an inequality, first you graph the line you would get from changing the < or > to an =. Can you see what the line is?

    • one year ago
  19. ilovenyc
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    @srossd |dw:1356666088705:dw|

    • one year ago
  20. ilovenyc
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    @srossd |dw:1356666151160:dw|

    • one year ago
  21. srossd
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    Alright, so what's the line, first?

    • one year ago
  22. ilovenyc
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    @srossd would it be -2

    • one year ago
  23. srossd
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    Well, you're looking for the equation of a line - you need more than a number. First of all, what's the slope (that is just a number)?

    • one year ago
  24. srossd
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    Oh, maybe I should be doing this @ilovenyc

    • one year ago
  25. ilovenyc
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    @srossd yeah i suck at algebra lol

    • one year ago
  26. srossd
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    No, I mean doing the @ilovenyc thing, but I'll help with the line too. It passes through the points (-2, 0) and (0, 3). The formula for slope is \[\frac{y_2-y_1}{x_2-x_1} = \frac{3-0}{0-(-2)} = \frac{3}{2}\] so the slope is 3/2. The y-intercept is 3, so the equation is y=3/2x+3. So now you're down to A and B - can you see which one it is?

    • one year ago
  27. srossd
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    (not a rhetorical question, tell me if you need help)

    • one year ago
  28. ilovenyc
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    @srossd B

    • one year ago
  29. srossd
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    Right, good job! (and I actually meant you had it down to B and C, hopefully you figured that out). Got any more problems I can help with?

    • one year ago
  30. ilovenyc
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    @srossd yeah i was wondering how could A, be the right answer lol, and yes i have more just like the one we just did.

    • one year ago
  31. srossd
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    Alright, lets see how much of this one you can do on your own. I'll be here to help, though.

    • one year ago
  32. ilovenyc
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    Which of the following inequalities matches the graph? (see attached photo) A y 3x - 5 B y < 3x - 5 C y < x - 5 D The correct inequality is not listed.

    • one year ago
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  33. srossd
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    Alright, so find the equation of the line first.

    • one year ago
  34. ilovenyc
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    C) y < 1/3x -5

    • one year ago
  35. ilovenyc
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    A) |dw:1356667093569:dw|

    • one year ago
  36. srossd
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    @ilovenyc So first, what's the slope of the line?

    • one year ago
  37. ilovenyc
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    0, and -2?

    • one year ago
  38. ilovenyc
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    @srossd 0, and -2?

    • one year ago
  39. srossd
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    @ilovenyc What do you mean?

    • one year ago
  40. ilovenyc
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    @srossd i think that is the slope of the line, i am not sure i told you i suck at alegbra

    • one year ago
  41. srossd
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    Don't worry, you'll get better with practice. Here's quick tutorial on finding slopes of lines: say you have a line. You can find the slope by picking two points, call them (x1,y1) and (x2,y2). Then you plug those numbers in to this formula: \[\frac{y_2-y_1}{x_2-x_1}\] So, in the last problem, I used the points (-2,0) and (0,3), and got 3/2. Another way to think about it is \[\frac{\textrm{rise}}{\textrm{run}}\] choose two points. The line goes up by some value (when it goes down, the value is negative), and it goes to the right by some value. Divide the two for slope. So, this can be your first practice: choose two points from the line dividing the shaded section and unshaded section, and find the slope. Tell me if you need help.

    • one year ago
  42. ilovenyc
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    @srossd find the slope from the graph?

    • one year ago
  43. srossd
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    Right, use the graph to see which points are on the line.

    • one year ago
  44. ilovenyc
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    (-6, and 0)

    • one year ago
  45. ilovenyc
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    -6

    • one year ago
  46. srossd
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    Well, -6 and 0 aren't points, they're just numbers. A point is something like (0,0) or (5,-3). So, what points lie on that line? Just name any 2.

    • one year ago
  47. ilovenyc
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    like (4, -8)

    • one year ago
  48. srossd
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    Actually, that point doesn't lie on the line, but (4,7) does. Can you see why?|dw:1356668074766:dw|

    • one year ago
  49. ilovenyc
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    yes i can

    • one year ago
  50. srossd
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    Great. So (4,7) is a point - can you find another?

    • one year ago
  51. ilovenyc
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    out of the graph? @srossd

    • one year ago
  52. srossd
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    Right, another point that lies on the line. Here http://assets.openstudy.com/updates/attachments/50dd0e0ae4b069916c86157f-ilovenyc-1356667034857-11.png, not my sketch of it.

    • one year ago
  53. srossd
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    And don't click that link, the comma messes it up.

    • one year ago
  54. ilovenyc
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    okay

    • one year ago
  55. srossd
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    @ilovenyc have you figured it out?

    • one year ago
  56. ilovenyc
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    (2,6)

    • one year ago
  57. srossd
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    Not quite - go over 2 on the x axis, and then go up until you hit the line. What y value are you at?|dw:1356668572509:dw|

    • one year ago
  58. ilovenyc
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    so would it be (2,10)

    • one year ago
  59. srossd
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    @ilovenyc No, it's (2,1) - was that a typo, or are you still confused?

    • one year ago
  60. ilovenyc
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    typo @srossd

    • one year ago
  61. srossd
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    Oh good, so you've got it now. So you have points (2,1) and (4,7). Here's the formula for slope again: \[\frac{y_2-y_1}{x_2-x_1}\] Can you try to apply it to those points?

    • one year ago
  62. srossd
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    Here's a hint: x_1 = 2, x_2 = 4, y_1 = 1, y_2 = 7.

    • one year ago
  63. srossd
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    Oh, and I should do the little message thing: @ilovenyc

    • one year ago
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