## ali2x2 one year ago Please solve the following inequality, showing all work and then list 3 numbers that are in the solution set. x/6 ≥ 3 In your own words: - Tell how to solve inequalities. Be specific and complete. - Tell how to graph inequalities. Be specific and complete. Please solve the following inequality, showing all work and then list 3 numbers that are in the solution set. x/6 + 4 ≥ 2

1. ali2x2

Hello?

2. Astrophysics

Hi, well what have you tried?

3. Astrophysics

$\frac{ x }{ 6 } \ge 3$ this should be an easy one, how would you solve for x?

4. ali2x2

Im not smart when it comes to this :/ @Astrophysics

5. Astrophysics

That's ok, just try your best I don't judge :)

6. Astrophysics

How would you go about isolating x in your question, it's just like normal algebra with a funny looking sign, that has a few extra rules, such as when you divide or multiply by negative, the sign flips :P

7. ali2x2

well i thought placeing 6 on the so it would be 6/6 = 1 but the 3 wins and that wouldnt be right

8. ali2x2

:P

9. Astrophysics

Hey do you know how to use the draw tool?

10. ali2x2

MHm

11. Astrophysics

|dw:1437028552079:dw| just show what you mean on here

12. Astrophysics

You can click on the drawing on top right, there should be a pencil

13. ali2x2

|dw:1437028576910:dw|

14. ali2x2

|dw:1437028595529:dw|

15. ali2x2

|dw:1437028608859:dw|

16. ali2x2

THats what i ment but it is wrong

17. Astrophysics

Mhm, well when doing algebra, you want to sort of balance things out, so it equals. What ever you do on one side you must always do to the other, and a really cool thing about algebra is, to do such things you just do the opposite operation of what already exists.

18. ali2x2

Amazing :P

19. Astrophysics

|dw:1437028694384:dw|

20. Astrophysics

See how that works?

21. ali2x2

Yes

22. Astrophysics

Since I multiplied the left side by 6 so I could get x alone, I also have to do the same on the right to balance it out.

23. ali2x2

6 cancel eachother out

24. ali2x2

then multiply 6 x 3

25. Astrophysics

Yes, what you do one side, you must do to the other, remember that :)

26. ali2x2

Ok :)

27. Astrophysics

Now solutions to the problem could be any integer that is greater than or equal to 18.

28. ali2x2

But how do i find that

29. Astrophysics

So you could even put $18 \ge 18$

30. ali2x2

But wouldnt that be 18 = 18

31. ali2x2

?

32. Astrophysics

Look at your problem, notice the symbol |dw:1437028879538:dw|

33. Astrophysics

The little line under the greater than means equal

34. ali2x2

XD oh i forgot.

35. Astrophysics

So we say greater than or equal to

36. Astrophysics

So you could say your solution set is [18,19,20] :)

37. ali2x2

Ok

38. ali2x2

Wait how did i get 18 19 and 20 i just add them there?

39. Astrophysics

40. ali2x2

Oh

41. Astrophysics

You could put any 3 numbers greater/ equal to 18...

42. ali2x2

:P

43. Astrophysics

Now, how would you graph that?

44. ali2x2

Can you stay here and see if i can get the next 2 correct?

45. ali2x2

46. Astrophysics

|dw:1437028983964:dw| here I made a graph for you, now graph the expression $x \ge 18$

47. Astrophysics

Yes, you must read your question carefully, it asks you to solve the inequality, get a solution set and graph.

48. ali2x2

THis is confusing O.o ??? I have no idea :(

49. Astrophysics

Ok, if I asked you to graph x = 18, how would you do that?

50. ali2x2

oh

51. ali2x2

|dw:1437029208610:dw| I DONT KNOWWWwwww

52. ali2x2

:(

53. ali2x2

I really wanna learn this

54. Astrophysics

No, that's not how you graph, compare it with mine, but x = 18 is just a vertical line. |dw:1437029309947:dw|

55. Astrophysics

Now you want greater than equal to, notice I made it a solid line for that purpose, when you have greater than/ less than with equal you make the line solid, when it's just greater/ less than than it's a dotted line.

56. Astrophysics

So we just shade in the area |dw:1437029385587:dw| that is $x \ge 18$

57. Astrophysics

To the right of the axis, as it's positive.

58. ali2x2

so if the "alligator" Is facing left the shading goes right

59. Astrophysics

Yes, but you should not think like that, you should know it means greater than.

60. ali2x2

Ok