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ilovenyc

  • one year ago

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

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  1. srossd
    • one year ago
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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|

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

  3. srossd
    • one year ago
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    Yeah, sure.

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

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

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

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

  8. srossd
    • one year ago
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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.

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

  10. srossd
    • one year ago
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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".

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

  12. srossd
    • one year ago
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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.

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

  14. srossd
    • one year ago
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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.

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

  16. srossd
    • one year ago
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    Yeah, definitely.

  17. ilovenyc
    • one year ago
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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.

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  18. srossd
    • one year ago
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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?

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

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

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

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

  23. srossd
    • one year ago
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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)?

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

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

  26. srossd
    • one year ago
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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?

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

  28. ilovenyc
    • one year ago
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    @srossd B

  29. srossd
    • one year ago
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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?

  30. ilovenyc
    • one year ago
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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.

  31. srossd
    • one year ago
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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.

  32. ilovenyc
    • one year ago
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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.

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

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

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

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

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

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

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

  40. ilovenyc
    • one year ago
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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

  41. srossd
    • one year ago
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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.

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

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

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

  45. ilovenyc
    • one year ago
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    -6

  46. srossd
    • one year ago
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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.

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

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

  49. ilovenyc
    • one year ago
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    yes i can

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

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

  52. srossd
    • one year ago
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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.

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

  54. ilovenyc
    • one year ago
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    okay

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

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

  57. srossd
    • one year ago
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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|

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

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

  60. ilovenyc
    • one year ago
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    typo @srossd

  61. srossd
    • one year ago
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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?

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

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

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