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

1. srossd

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

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

3. srossd

Yeah, sure.

4. ilovenyc

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

5. srossd

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

6. ilovenyc

|dw:1356665051133:dw|

7. ilovenyc

8. srossd

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

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

10. srossd

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

11. ilovenyc

12. srossd

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

okay and can you write out part 2 please @srossd

14. srossd

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

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

16. srossd

Yeah, definitely.

17. ilovenyc

@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

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

@srossd |dw:1356666088705:dw|

20. ilovenyc

@srossd |dw:1356666151160:dw|

21. srossd

Alright, so what's the line, first?

22. ilovenyc

@srossd would it be -2

23. srossd

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

Oh, maybe I should be doing this @ilovenyc

25. ilovenyc

@srossd yeah i suck at algebra lol

26. srossd

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

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

28. ilovenyc

@srossd B

29. srossd

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

@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

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

32. ilovenyc

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

Alright, so find the equation of the line first.

34. ilovenyc

C) y < 1/3x -5

35. ilovenyc

A) |dw:1356667093569:dw|

36. srossd

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

37. ilovenyc

0, and -2?

38. ilovenyc

@srossd 0, and -2?

39. srossd

@ilovenyc What do you mean?

40. ilovenyc

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

41. srossd

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

@srossd find the slope from the graph?

43. srossd

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

44. ilovenyc

(-6, and 0)

45. ilovenyc

-6

46. srossd

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

like (4, -8)

48. srossd

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

49. ilovenyc

yes i can

50. srossd

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

51. ilovenyc

out of the graph? @srossd

52. srossd

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

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

54. ilovenyc

okay

55. srossd

@ilovenyc have you figured it out?

56. ilovenyc

(2,6)

57. srossd

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

so would it be (2,10)

59. srossd

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

60. ilovenyc

typo @srossd

61. srossd

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

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

63. srossd

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