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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

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  1. anonymous
    • one year ago
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    @AbdullahM

  2. anonymous
    • one year ago
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    1. x> -6

  3. AbdullahM
    • one year ago
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    correct :)

  4. anonymous
    • one year ago
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    how would i graph this

  5. AbdullahM
    • one year ago
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    |dw:1435336629065:dw|

  6. AbdullahM
    • one year ago
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    You could use: https://www.desmos.com/calculator

  7. anonymous
    • one year ago
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    i mean on a number line sorry

  8. anonymous
    • one year ago
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    it would be an open circle?

  9. AbdullahM
    • one year ago
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    yes

  10. anonymous
    • one year ago
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    Do you have a website for the number line?

  11. AbdullahM
    • one year ago
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    essentially, you can use the website and only look at the x-axis

  12. AbdullahM
    • one year ago
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    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
    • one year ago
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    ok so closed

  14. AbdullahM
    • one year ago
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    |dw:1435336897914:dw| this has a dashed line so it means open circle

  15. AbdullahM
    • one year ago
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    I drew an orange box around the dashed line.

  16. anonymous
    • one year ago
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    alright i can graph the rest i just need help solving the rest

  17. anonymous
    • one year ago
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    -2x +1 < -11 \[-2x +1 \le -11\]

  18. AbdullahM
    • one year ago
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    for graphing it on a number line: |dw:1435337002162:dw|

  19. AbdullahM
    • one year ago
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    For #2, we would first take the +1 to the other side. So we have to subtract that on both sides.

  20. anonymous
    • one year ago
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    so -12

  21. anonymous
    • one year ago
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    -2x less than or equal to -12

  22. AbdullahM
    • one year ago
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    now we have \(\sf -2x\le -12\)

  23. anonymous
    • one year ago
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    now devide -2?

  24. anonymous
    • one year ago
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    divide*

  25. AbdullahM
    • one year ago
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    Do you know that when you divide by a negative number on both sides that the sign flips

  26. anonymous
    • one year ago
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    so it goes to >?

  27. anonymous
    • one year ago
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    or this

  28. AbdullahM
    • one year ago
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    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
    • one year ago
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    does it ever switch from \[\le \to \]

  30. anonymous
    • one year ago
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    not showign up

  31. anonymous
    • one year ago
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    without the line under it

  32. AbdullahM
    • one year ago
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    no it can't

  33. anonymous
    • one year ago
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    but this answer is x=6

  34. AbdullahM
    • one year ago
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    \(\color{blue}{\text{Originally Posted by}}\) @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
    • one year ago
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    x= 6

  36. anonymous
    • one year ago
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    oh x > 6

  37. AbdullahM
    • one year ago
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    no, it would be \(\sf\Large x\ge6\)

  38. anonymous
    • one year ago
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    yeah thats i meant my b

  39. anonymous
    • one year ago
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    could i also say greater than or equal to?

  40. AbdullahM
    • one year ago
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    remember these are the opposites: \(\sf \le\) and \(\sf \ge\) are opposites < and > are opposites

  41. anonymous
    • one year ago
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    and this circle would be open?

  42. AbdullahM
    • one year ago
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    nope closed

  43. AbdullahM
    • one year ago
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    http://prntscr.com/7ln08a from: http://www.studyzone.org/mtestprep/math8/a/graphing_inequalities7l.cfm

  44. anonymous
    • one year ago
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    |dw:1435337698545:dw|

  45. anonymous
    • one year ago
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    @AbdullahM

  46. AbdullahM
    • one year ago
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    correct :)

  47. anonymous
    • one year ago
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    10 < -3x + 1

  48. anonymous
    • one year ago
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    -1 both sides

  49. anonymous
    • one year ago
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    9 < -3x

  50. AbdullahM
    • one year ago
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    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
    • one year ago
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    oh alright

  52. anonymous
    • one year ago
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    +3x both sides 3x + 10 < 1 3x < -9 x< -3

  53. anonymous
    • one year ago
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    |dw:1435338193021:dw|

  54. anonymous
    • one year ago
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    @AbdullahM

  55. anonymous
    • one year ago
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    i might have made a mistake

  56. anonymous
    • one year ago
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    Should i have flipped the sign?

  57. AbdullahM
    • one year ago
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    splendid work, you made no mistakes :)

  58. AbdullahM
    • one year ago
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    we only flip the sign when we divide by a negative number

  59. anonymous
    • one year ago
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    oh alright

  60. AbdullahM
    • one year ago
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    2(x + 5) > 8x – 8

  61. anonymous
    • one year ago
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    2(x + 5) > 8x - 8

  62. AbdullahM
    • one year ago
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    First we have to take care of 2(x+5) distribute the 2 inside

  63. anonymous
    • one year ago
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    2x + 10 > 8x - 8

  64. anonymous
    • one year ago
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    -8x both sides -6x + 10 > -8 -10 both sides -6x> -18 divide -6 both sides x < 3

  65. anonymous
    • one year ago
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    |dw:1435338649893:dw|

  66. AbdullahM
    • one year ago
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    wow, amazing work once again! :D

  67. anonymous
    • one year ago
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    Thank you :)

  68. anonymous
    • one year ago
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    -2(x - 3) > 5 - (x +3)

  69. AbdullahM
    • one year ago
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    –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
    • one year ago
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    -2x + 6 > 5 -x - 3 @AbdullahM ?

  71. AbdullahM
    • one year ago
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    amazing work! :D

  72. AbdullahM
    • one year ago
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    no we can add the 2x to both sides and work from there :)

  73. anonymous
    • one year ago
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    why te 2x?

  74. anonymous
    • one year ago
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    +x both sides -x + 6 > 5-3 -6 both sides -x > -4 divide by -1 x < 4

  75. AbdullahM
    • one year ago
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    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
    • one year ago
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    not really a rtick, more like a rule xD

  77. anonymous
    • one year ago
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    yeah :p i thought it' be easier

  78. AbdullahM
    • one year ago
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    great work again :)

  79. anonymous
    • one year ago
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    |dw:1435339061662:dw|

  80. anonymous
    • one year ago
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    @AbdullahM

  81. anonymous
    • one year ago
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    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
    • one year ago
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    \(\color{blue}{\text{Originally Posted by}}\) @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
    • one year ago
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    alright and i think i did my last graph wrong

  84. anonymous
    • one year ago
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    |dw:1435339286981:dw|

  85. AbdullahM
    • one year ago
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    open circle, not closed. and everything else is correct

  86. anonymous
    • one year ago
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    @AbdullahM Thank you for the help! You are a great teacher :)

  87. AbdullahM
    • one year ago
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    anytime, that's why I'm on OpenStudy to help.

  88. anonymous
    • one year ago
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    That's all i need for today but i'll hit ya up if i need help another time, Have a good afternoon!

  89. AbdullahM
    • one year ago
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    sure :)

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