## anonymous 5 years ago I need some help understanding clearing fractions. Example: -x+2/5=5-4/3x

1. anonymous

-x+2/5=5-4/3x

2. anonymous

Is the equation a) $$-x + \frac{2}{5} = 5 - \frac{4}{3x}$$ b) $$\frac{-x + 2}{5} = 5- \frac{4}{3x}$$ c) None of the above.

3. anonymous

a)

4. anonymous

the x is not below the 4

5. anonymous

oh, good. That's even better.

6. anonymous

$-x + \frac{2}{5} = 5 - \frac{4}{3}x$

7. anonymous

Right?

8. anonymous

Yes

9. anonymous

Ok, so lets start by getting all of our 'like' terms to have the same denominator. To do that, we'll make the -x into a fraction with a 3 on bottom. How can we do that?

10. anonymous

-x/3

11. anonymous

Nearly, but it must maintain equivalence. 3/3 is 1 right?

12. anonymous

-1x/3

13. anonymous

No. Stop guessing and listen. 3/3 = 1. Right?

14. anonymous

yes

15. anonymous

Ok, and 1 times any number gives you the same number right? a*1 = a

16. anonymous

right

17. anonymous

so then: $a = 1*a = \frac{3}{3}*a = \frac{3a}{3} = a$

18. anonymous

Did you follow that? Sometimes it's hard to read on one line.

19. anonymous

yes

20. anonymous

Ok, so what is -x as a multiple of 1/3?

21. anonymous

The basic rule of thumb for equivalent fractions is: You can multiply the top and bottom by the same thing and the value doesn't change.

22. anonymous

don't know

23. anonymous

So we have: $\frac{-x}{1}$ And we want to get a 3 on the bottom, so we multiply the bottom times 3. That means we have to multiply the top by 3 also to keep it having the same value as -x.

24. anonymous

$\frac{-3x}{3} = -x$ Right?

25. anonymous

-3x/3

26. anonymous

Right.

27. anonymous

So lets do the same thing to the 5 on the right side of the equation. We need to get a 5 on bottom, so what would it be.. We have: $\frac{5}{1}$

28. anonymous

5/1+2/5

29. anonymous

Ok, we have this (after changing the denominator on -x) $\frac{-3x}{3} + \frac{2}{5} = 5 -\frac{4x}{3}$

30. anonymous

Can you use algebra to get all the terms with x on one side, and all the terms without x on the other?

31. anonymous

I appreciate you trying to help me, but I need to see the example I gave solved from the beginning to the end. It isn't working very well showing me a step here and there.

32. anonymous

Hello

33. anonymous

One second.

34. anonymous

Starting from $\frac{-3x}{3} + \frac{2}{5} = 5 - \frac{4x}{3}$ Can you solve for x?

35. anonymous

James are you there?

36. anonymous

-x+2/5=5-4x/3

37. anonymous

Because you have denominators and an = sign, you need to find a common denominator. What is the common denominator using 5 and 3

38. anonymous

15

39. anonymous

So multiply the whole equation by 15.

40. anonymous

Yes.. every term.

41. anonymous

15(-x+2/5)=15(5-4/3x)

42. anonymous

Yep. And distribute.

43. anonymous

(15)(-x) + (15)(2) (15)(5) - (15)(4x) ----- = ------- 5 3

44. anonymous

Cancel out the denominators into the numerators.

45. anonymous

(15)(-x) + (3)(2) = (15)(5) - 5(4x)

46. anonymous

-15x + 6 = 75 - 20x

47. anonymous

Now solve for x in the usual way.

48. anonymous

Blexting, let him do it.

49. anonymous

I don't know

50. anonymous

James when you are solving and you see x's on both sides of the equation, I like to get rid of the smallest one. Which one is smaller -15x or -20x

51. anonymous

-20x

52. anonymous

so add 20x to both sides

53. anonymous

James, if you have an equation: 5x + 4 = 4 How do you solve for x?

54. anonymous

What do you get James when you +20x to both sides?

55. anonymous

20x-15x+6=75-20x=20X

56. anonymous

THE LAST ONE should be a plus sign

57. anonymous

58. anonymous

-5x+6=75-x

59. anonymous

20x - 15x (20 - 15 = ?)

60. anonymous

-20x + 20x = (-20 + 20 = ?)

61. anonymous

5

62. anonymous

So you have 5x + 6 = 75 (because your -20 + 20 = 0 so you don't have any x's on that side)

63. anonymous

Then what?

64. anonymous

how do you get the x by itself.. do you get rid of the 5 first or the 6 first?

65. anonymous

5x=75-6

66. anonymous

Yes... but what is 75-6 5x = 69

67. anonymous

but isn't the answer suppose to be x=69/5 and how do you get that?

68. anonymous

Yes... divide in you calculator. 13.8

69. anonymous

where are you getting 13.8

70. anonymous

Once again, I appreciate the help, but I need to see the problem solved from beginning to end. It isn't helping trying to get me to figure out something I don't know. I have to see it work.

71. anonymous

would it be 5x-69 x=69÷5 x=69/5

72. anonymous

5x=69 x=69÷5 x=69/5

73. anonymous

Hello, is anybody there?

74. anonymous

I don't appreciate being ignored. Just because I don't understand doesn't mean I should not be helped. If I knew this crap I wouldn't be here in the first place. Thanks for nothing, and I will not recommend this place to anyone.

75. anonymous

James, nobody knows that you entered another comment on this page unless they are sitting here watching your post... You need to go and "ask a question" and someone will see it and respond...

Find more explanations on OpenStudy