Question

how do you solve this:

2x-3 = (3+x)/2

Answer 1

multiply by 2, subtract an x and add a 3

Answer 2

thank you

Answer 3

x=3

Answer 4

i need the process, not the answer which i already know

Answer 5

I don't think so

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

thank you so much, i understand now

Answer 10

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

Answer 11

do i get a medal :)

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

the second one

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

Pick a term, any term.

Answer 25

3x

Answer 26

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

Answer 27

But that's ok!

Answer 28

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

Answer 29

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

Answer 30

3-9x?

Answer 31

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

Answer 32

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

Answer 33

i'm not sure...

Answer 34

a(b+c) = ab + ac

Right? Basic multiplicative distribution

Answer 35

ok so would it be 5/3 -x?

Answer 36

yes

Answer 37

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

Answer 38

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

Answer 39

Yes

Answer 40

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

Answer 41

maybe a little more

Answer 42

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

Answer 43

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

Answer 44

You can certainly do that yes.

Answer 45

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

Answer 46

ok so how do you do it?

Answer 47

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

Answer 48

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

Answer 49

We do this using the trick of multiplying by 1.

Answer 50

\(4 \times 1 = ?\)

Answer 51

4

Answer 52

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

Answer 53

right

Answer 54

Ok, so what is \(\frac{3}{3}\)

Answer 55

1

Answer 56

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

Answer 57

\[4\times \frac{3}{3} = \frac{4\times 3}{3} = \frac{12}{3}\]

Answer 58

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

Answer 59

Did you follow that?

Answer 60

yes
so the answer would be 17/3

Answer 61

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

Answer 62

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

Answer 63

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

Answer 64

Certainly

Answer 65

it would be 3x = 1 17/3?

Answer 66

yeah, but I dun like mixed numbers

Answer 67

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

Answer 68

isn't it 20/9?

Answer 69

x = 20/9 is correct yes.

Answer 70

you don't divide that by 3?

Answer 71

Huh? we did already

Answer 72

It was 3x = 20/3

Answer 73

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

Answer 74

\(3x = 1+\frac{17}{3}\)\[\implies 3x = 1\times \frac{3}{3} + \frac{17}{3}\]\[\implies 3x = \frac{1\times 3}{3} + \frac{17}{3}\]\[\implies 3x = \frac{3}{3} + \frac{17}{3}\]\[\implies 3x = \frac{20}{3}\]

Answer 75

Then you divide by 3 on both sides

Answer 76

Follow all that?

Answer 77

yes thanks

Answer 78

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

Answer 79

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

Answer 80

wouldn't the answer be different?

Answer 81

nope.
\[3x \times \frac{1}{3} = \frac{20}{3} \times \frac{1}{3}\]
\[x = \frac{20}{9} \]


\[3x \div 3 = \frac{20}{3} \div 3\]
\[x = 6.\bar{6}\bar{6} \div 3 = 2.\bar{2}\bar{2} = \frac{20}{9}\]