## ilovenyc Group Title -7y - 17 > 11 Part 1: Solve the inequality above. Part 2: Describe the graph of the solution. one year ago one year ago

1. srossd Group Title

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 Group Title

@srossd thank you so much! can you help me with another

3. srossd Group Title

Yeah, sure.

4. ilovenyc Group Title

2x + 1 5 or -3x > -9 Part 1: Solve the inequality above. Part 2: Describe the graph of the solution.

5. srossd Group Title

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

6. ilovenyc Group Title

|dw:1356665051133:dw|

7. ilovenyc Group Title

8. srossd Group Title

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 Group Title

And same to you, tell me if you have trouble reading.

10. srossd Group Title

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

11. ilovenyc Group Title

12. srossd Group Title

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 Group Title

okay and can you write out part 2 please @srossd

14. srossd Group Title

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 Group Title

@srossd THANKS SO MUCH! can you help me with some more?

16. srossd Group Title

Yeah, definitely.

17. ilovenyc Group Title

@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.

18. srossd Group Title

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 Group Title

@srossd |dw:1356666088705:dw|

20. ilovenyc Group Title

@srossd |dw:1356666151160:dw|

21. srossd Group Title

Alright, so what's the line, first?

22. ilovenyc Group Title

@srossd would it be -2

23. srossd Group Title

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 Group Title

Oh, maybe I should be doing this @ilovenyc

25. ilovenyc Group Title

@srossd yeah i suck at algebra lol

26. srossd Group Title

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 Group Title

(not a rhetorical question, tell me if you need help)

28. ilovenyc Group Title

@srossd B

29. srossd Group Title

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 Group Title

@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 Group Title

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

32. ilovenyc Group Title

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.

33. srossd Group Title

Alright, so find the equation of the line first.

34. ilovenyc Group Title

C) y < 1/3x -5

35. ilovenyc Group Title

A) |dw:1356667093569:dw|

36. srossd Group Title

@ilovenyc So first, what's the slope of the line?

37. ilovenyc Group Title

0, and -2?

38. ilovenyc Group Title

@srossd 0, and -2?

39. srossd Group Title

@ilovenyc What do you mean?

40. ilovenyc Group Title

@srossd i think that is the slope of the line, i am not sure i told you i suck at alegbra

41. srossd Group Title

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 Group Title

@srossd find the slope from the graph?

43. srossd Group Title

Right, use the graph to see which points are on the line.

44. ilovenyc Group Title

(-6, and 0)

45. ilovenyc Group Title

-6

46. srossd Group Title

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 Group Title

like (4, -8)

48. srossd Group Title

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

49. ilovenyc Group Title

yes i can

50. srossd Group Title

Great. So (4,7) is a point - can you find another?

51. ilovenyc Group Title

out of the graph? @srossd

52. srossd Group Title

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 Group Title

And don't click that link, the comma messes it up.

54. ilovenyc Group Title

okay

55. srossd Group Title

@ilovenyc have you figured it out?

56. ilovenyc Group Title

(2,6)

57. srossd Group Title

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 Group Title

so would it be (2,10)

59. srossd Group Title

@ilovenyc No, it's (2,1) - was that a typo, or are you still confused?

60. ilovenyc Group Title

typo @srossd

61. srossd Group Title

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 Group Title

Here's a hint: x_1 = 2, x_2 = 4, y_1 = 1, y_2 = 7.

63. srossd Group Title

Oh, and I should do the little message thing: @ilovenyc