## anonymous 5 years ago how do you solve this: 2x-3 = (3+x)/2

1. anonymous

multiply by 2, subtract an x and add a 3

2. anonymous

thank you

3. anonymous

x=3

4. anonymous

5. anonymous

I don't think so

6. anonymous

The point is, you want to get all your x terms on one side and your non-variable terms on the other

7. anonymous

$2*(2x-3)=[(3+x)/2]*2$

8. anonymous

then it goes to : 4x-6=3+x

9. anonymous

thank you so much, i understand now

10. anonymous

the get x by itself...so subtract -x to the left so next step: 3x=9

11. anonymous

do i get a medal :)

12. anonymous

yes! but i don't know how to give one

13. anonymous

i need help with this one too please: 2x-1= 1/3(5-3x) + 4

14. anonymous

Ok, well why don't you tell us how to start this one

15. anonymous

Oh, and is it $\frac{1}{3(5-3x)}$ or $\frac{1}{3}(5-3x)$

16. anonymous

the second one

17. anonymous

Ok. So which part do you want to tackle first? (There's lots of different paths to the same answer)

18. anonymous

Overall goal is to get all the x terms on one side and the non-x terms on the other side

19. anonymous

You tell me what to do, and I'll write the new equation.

20. anonymous

$2x-1= \frac{1}{3}(5-3x) + 4$

21. anonymous

i don't know how to start that's why i'm asking

22. anonymous

That's ok. Just pick a term that is in the wrong place

23. anonymous

We want everything with an x on the left, and everything without an x on the right

24. anonymous

Pick a term, any term.

25. anonymous

3x

26. anonymous

Ah, that term is a little tricky because it's part of a factor in a product. We will need to expand that product out first before we can work with that term directly

27. anonymous

But that's ok!

28. anonymous

That just means we need to distribute the 1/3 to each of the terms in the other factor

29. anonymous

So what do we get when we distribute that 1/3?

30. anonymous

3-9x?

31. anonymous

no. we have to multiply each term in the left factor by 1/3 $\frac{1}{3}(5-3x) = \frac{1}{3}*5 - \frac{1}{3}*3x$

32. anonymous

Does that make sense? So what do we have when we simplify that product?

33. anonymous

i'm not sure...

34. anonymous

a(b+c) = ab + ac Right? Basic multiplicative distribution

35. anonymous

ok so would it be 5/3 -x?

36. anonymous

yes

37. anonymous

So now we have: $2x-1= \frac{5}{3}-x + 4$

38. anonymous

so the whole thing would be : 2x-1 = 5/3-x+4?

39. anonymous

Yes

40. anonymous

Can you solve from there? or do you need more help with it?

41. anonymous

maybe a little more

42. anonymous

Ok, so pick a term that's in the wrong place

43. anonymous

how would i combine 5/3 + 4 that's the next step right?

44. anonymous

You can certainly do that yes.

45. anonymous

There is no 'next step'. There are a lot of ways to do it. If you want to do that next, go for it =)

46. anonymous

ok so how do you do it?

47. anonymous

How do you add $$\frac{5}{3} + 4$$

48. anonymous

You have to change the denominator of the 4 to match the 3 in the 5/3

49. anonymous

We do this using the trick of multiplying by 1.

50. anonymous

$$4 \times 1 = ?$$

51. anonymous

4

52. anonymous

Ok, so if we multiply by 1 we won't have changed the value, right?

53. anonymous

right

54. anonymous

Ok, so what is $$\frac{3}{3}$$

55. anonymous

1

56. anonymous

So you're saying then that if I multiply 4 by 3/3 I will still have 4?

57. anonymous

$4\times \frac{3}{3} = \frac{4\times 3}{3} = \frac{12}{3}$

58. anonymous

And 12/3 does equal 4, but it's in a different form that is now easy to add to 5/3

59. anonymous

60. anonymous

yes so the answer would be 17/3

61. anonymous

Well, the sum of those two terms would be 17/3 yes

62. anonymous

So we have: $2x-1= \frac{17}{3}-x$

63. anonymous

then irt would be 3x-1= 17/3

64. anonymous

Certainly

65. anonymous

it would be 3x = 1 17/3?

66. anonymous

yeah, but I dun like mixed numbers

67. anonymous

Can you do the same trick to the 1 we did to the 4 to make it easy to add to the 17/3

68. anonymous

isn't it 20/9?

69. anonymous

x = 20/9 is correct yes.

70. anonymous

you don't divide that by 3?

71. anonymous

72. anonymous

It was 3x = 20/3

73. anonymous

oh ok i thought it was 3x = 1 17/3? and then you divide by 3 on both sides to get x

74. anonymous

$$3x = 1+\frac{17}{3}$$$\implies 3x = 1\times \frac{3}{3} + \frac{17}{3}$$\implies 3x = \frac{1\times 3}{3} + \frac{17}{3}$$\implies 3x = \frac{3}{3} + \frac{17}{3}$$\implies 3x = \frac{20}{3}$

75. anonymous

Then you divide by 3 on both sides

76. anonymous

77. anonymous

yes thanks

78. anonymous

but how do you divide 3 on both sides, that what i want to know

79. anonymous

dividing by 3 is the same as multiplying by 1/3

80. anonymous

nope. $3x \times \frac{1}{3} = \frac{20}{3} \times \frac{1}{3}$ $x = \frac{20}{9}$ $3x \div 3 = \frac{20}{3} \div 3$ $x = 6.\bar{6}\bar{6} \div 3 = 2.\bar{2}\bar{2} = \frac{20}{9}$