## anonymous 5 years ago -7(x+4)9x<2(2x-8)-3x solve the inequality help not very good at math

1. anonymous

Distrubute the factors and multiply it out. Then simplify. Treat the inequality just as you would an equal side. The only tricky thing to remember is if you divide by a negative you have to change which way the inequality goes.

2. amistre64

is the equation correct as stated?

3. anonymous

yes

4. anonymous

Do you know how to do the distribution step?

5. amistre64

-36x(x+4) > 4x - 16 - 3x -36x^2 - 144x > x-16 is correct?

6. anonymous

no i dont not very good at algebra and to u amistre i think so

7. amistre64

lets figure out what I did :) lets start with an easy example... 3(8) = 24 right?

8. anonymous

yes

9. amistre64

then: 3(6+2) should also equal 24 right?

10. anonymous

yes

11. amistre64

then this should also work for us: 3(6) + 3(2) = 24 18 + 6 = 24 24 = 24 .... do you see that? its called the distributive property and it allows us to "distribute" the 3 thru the (6+2) to get the answer.

12. anonymous

oh ok i understand now

13. amistre64

2(2x-8) distribute this for me then :)

14. anonymous

4x-16

15. amistre64

very good :)

16. amistre64

17. anonymous

-7x-28

18. amistre64

excellent work..... see how easy that is :)

19. anonymous

yes i do

20. amistre64

that left side has one more "distribution" to take care of: 9x(-7x-28) is what? I know you can do this...

21. anonymous

-56x-252

22. amistre64

look over your "multiplication" work again and try that again.... 9x(-7x) +9x(-28) ....

23. anonymous

wait i meant -63x-252

24. anonymous

i see what mistake i made

25. amistre64

very good, but remember to include the "x". x(x) = x^2 ; which means x squared.

26. amistre64

-63x^2 -252x ..... ok?

27. anonymous

-63x2-252x right?

28. amistre64

that is correct.... -63x^2 -252x < 4x -16 -3x is what we are up to now.... do you know what we should do now?

29. anonymous

simplify

30. amistre64

we can simplify this to some extent yes, we can "combine" like terms..

31. amistre64

-63^2 -252x < 4x-3x -16 -63x^2 -252x < x -16 Do you know how to move things from one side to the other? Its important to be able to do this while keeping the balance between them the same.... does that make sense?

32. anonymous

yes it makes sense i think i do how to move one side to the the other

33. amistre64

let me give you an easy example to remind you: 10 < 15 right? then 1+2+3+4 < 4+5+6 right?

34. anonymous

yes

35. amistre64

to keep everything in balance...whatever we "add" or "remove" from one side has to be done to the other.... right? lets subtract "4" from each side 1+2+3+4 -4 < 4+5+6 -4 1+2+3 < 5+6 ; 6>11

36. anonymous

that make sense

37. amistre64

i flipped my sign around didnt i....

38. anonymous

yeah.

39. amistre64

its these fat fingers and this tiny little keyboard :)

40. anonymous

lol its ok i do that to

41. amistre64

-63x^2 -252x < x -16 lets make the lefthand side = 0, to do that we need to "add" their value to both sides

42. amistre64

-63x^2 [+63x^2] -252x [+252x] < [+63x^2] +x [+252x]-16

43. amistre64

0< 63x^2 +253x -16 is what we get right?

44. anonymous

yes thats what i got

45. amistre64

now comes the hard part, because it gets a little on the "advanced" side of things for this one..... but we can use a formula called the "quadratic" formula to find the values for "x" that make this equal to zero... wanna try it out?

46. anonymous

yes

47. amistre64

ok.... notive that we have numbers in front of all of our "terms". they are 63, 253, and -16. we want to use these in our quadratic formula....

48. anonymous

ok

49. amistre64

-253 + sqrt(253^2 - (4)(-16)(63)) ------------------------------ 2(63) this aint gonna be pretty :)

50. anonymous

is sqrt is square rIght?

51. amistre64

yes, sqrt() is what I use to indicate the square root "umbrella" and everything inside of the () is what is under the "umbrella".

52. amistre64

where ever did you get this inequality at? its almost a nightmare :)

53. anonymous

its on a study guide but i have to go my computer is missing up thanxs for the help

54. amistre64