## anonymous one year ago 1. x – 3 > –9 2. –2x + 1 ≤ –11 3. 10 < –3x + 1 4. 2(x + 5) > 8x – 8 5. –2(x – 3) ≥ 5 – (x + 3) Solve each and graph for each

1. anonymous

@AbdullahM

2. anonymous

1. x> -6

3. AbdullahM

correct :)

4. anonymous

how would i graph this

5. AbdullahM

|dw:1435336629065:dw|

6. AbdullahM

You could use: https://www.desmos.com/calculator

7. anonymous

i mean on a number line sorry

8. anonymous

it would be an open circle?

9. AbdullahM

yes

10. anonymous

Do you have a website for the number line?

11. AbdullahM

essentially, you can use the website and only look at the x-axis

12. AbdullahM

and since you see the graph has a dashed line, that means an open circle. When the line on the graph is solid, then that means a closed circle.

13. anonymous

ok so closed

14. AbdullahM

|dw:1435336897914:dw| this has a dashed line so it means open circle

15. AbdullahM

I drew an orange box around the dashed line.

16. anonymous

alright i can graph the rest i just need help solving the rest

17. anonymous

-2x +1 < -11 $-2x +1 \le -11$

18. AbdullahM

for graphing it on a number line: |dw:1435337002162:dw|

19. AbdullahM

For #2, we would first take the +1 to the other side. So we have to subtract that on both sides.

20. anonymous

so -12

21. anonymous

-2x less than or equal to -12

22. AbdullahM

now we have $$\sf -2x\le -12$$

23. anonymous

now devide -2?

24. anonymous

divide*

25. AbdullahM

Do you know that when you divide by a negative number on both sides that the sign flips

26. anonymous

so it goes to >?

27. anonymous

or this

28. AbdullahM

For example: $$\sf\Large -x \le 5$$ then $$\sf\Large x \ge 5$$ another example: $$\sf\Large -2y > 6$$ then $$\sf\Large y<-3$$

29. anonymous

does it ever switch from $\le \to$

30. anonymous

not showign up

31. anonymous

without the line under it

32. AbdullahM

no it can't

33. anonymous

34. AbdullahM

$$\color{blue}{\text{Originally Posted by}}$$ @AbdullahM now we have $$\sf -2x\le -12$$ $$\color{blue}{\text{End of Quote}}$$ if we divide -2, and also we have to change the sign, what do we get?

35. anonymous

x= 6

36. anonymous

oh x > 6

37. AbdullahM

no, it would be $$\sf\Large x\ge6$$

38. anonymous

yeah thats i meant my b

39. anonymous

could i also say greater than or equal to?

40. AbdullahM

remember these are the opposites: $$\sf \le$$ and $$\sf \ge$$ are opposites < and > are opposites

41. anonymous

and this circle would be open?

42. AbdullahM

nope closed

43. AbdullahM
44. anonymous

|dw:1435337698545:dw|

45. anonymous

@AbdullahM

46. AbdullahM

correct :)

47. anonymous

10 < -3x + 1

48. anonymous

-1 both sides

49. anonymous

9 < -3x

50. AbdullahM

10 < –3x + 1 lets make our life easier and not have to do the switching signs. So lets take 3x to the other side by addition

51. anonymous

oh alright

52. anonymous

+3x both sides 3x + 10 < 1 3x < -9 x< -3

53. anonymous

|dw:1435338193021:dw|

54. anonymous

@AbdullahM

55. anonymous

i might have made a mistake

56. anonymous

Should i have flipped the sign?

57. AbdullahM

splendid work, you made no mistakes :)

58. AbdullahM

we only flip the sign when we divide by a negative number

59. anonymous

oh alright

60. AbdullahM

2(x + 5) > 8x – 8

61. anonymous

2(x + 5) > 8x - 8

62. AbdullahM

First we have to take care of 2(x+5) distribute the 2 inside

63. anonymous

2x + 10 > 8x - 8

64. anonymous

-8x both sides -6x + 10 > -8 -10 both sides -6x> -18 divide -6 both sides x < 3

65. anonymous

|dw:1435338649893:dw|

66. AbdullahM

wow, amazing work once again! :D

67. anonymous

Thank you :)

68. anonymous

-2(x - 3) > 5 - (x +3)

69. AbdullahM

–2(x – 3) ≥ 5 – (x + 3) this time we have both sides where we have to dsitribute. Be careful, they have a negative number outside that needs to be distributed

70. anonymous

-2x + 6 > 5 -x - 3 @AbdullahM ?

71. AbdullahM

amazing work! :D

72. AbdullahM

no we can add the 2x to both sides and work from there :)

73. anonymous

why te 2x?

74. anonymous

+x both sides -x + 6 > 5-3 -6 both sides -x > -4 divide by -1 x < 4

75. AbdullahM

so we don't have to divide by a negative number on both sides, but it seems like you have mastered that trick anyways :D

76. AbdullahM

not really a rtick, more like a rule xD

77. anonymous

yeah :p i thought it' be easier

78. AbdullahM

great work again :)

79. anonymous

|dw:1435339061662:dw|

80. anonymous

@AbdullahM

81. anonymous

Explain, in complete sentences, when you would use an open circle or a closed circle, and when you would shade to the right or left, to graph an inequality on the number line. (3 points) 7. Describe a real life scenario where inequalities are used and state the inequality. (2 points)

82. AbdullahM

$$\color{blue}{\text{Originally Posted by}}$$ @AbdullahM http://prntscr.com/7ln08a from: http://www.studyzone.org/mtestprep/math8/a/graphing_inequalities7l.cfm $$\color{blue}{\text{End of Quote}}$$ use this for the first question

83. anonymous

alright and i think i did my last graph wrong

84. anonymous

|dw:1435339286981:dw|

85. AbdullahM

open circle, not closed. and everything else is correct

86. AbdullahM
87. anonymous

@AbdullahM Thank you for the help! You are a great teacher :)

88. AbdullahM

anytime, that's why I'm on OpenStudy to help.

89. anonymous

That's all i need for today but i'll hit ya up if i need help another time, Have a good afternoon!

90. AbdullahM

sure :)