Question

In linear equations, how do i know if i should subtract from the right side or the left side?

Answer 1

example..

Answer 2

I like my coefficient for x to remain positive; therefore, if I have

2x + 10 = 12x

I subtract 2x from the left side and if I have

12x + 10 = 2x

I subtract 2x from the right side

Answer 3

3x + 7 = 10x +5
7 = 7x +5
- ^here? ^ or here?

Answer 4

it really doesn't matter so long as you keep the goal in mind:
get x by itself
pick one and we can continue from there

Answer 5

And how much do i subtract? the whole number or so it remains +/-0?

Answer 6

Ok

Answer 7

so i got 0=7x-2

Answer 8

now i need to divide -2 by 7?

Answer 9

no, we need the 2 on the other side of the equation
that's what I mean about getting x by itself

Answer 10

Ok so i dont do 0=7x-2?

Answer 11

if we divide by 7 now we get\[0=x-\frac{2}{7}\]which is okay, we can still solve it from here; but it's a good policy to leave fractions for the end if possible.
so instead add 2 to both sides to make x a little bit more alone.

Answer 12

I dont get it, i get like 0.29..

Answer 13

leave the answer in fraction form

Answer 14

Oh i see, so i get 2=7x?

Answer 15

right, now we divide by 7 to isolate x
what is x=?
(leave as a fraction)

Answer 16

I dont know.. 2/7?

Answer 17

you do know!
lol
shall we do another?

Answer 18

If you want more info, watch this and the next 2 videos
http://www.khanacademy.org/video/simple-equations?playlist=Algebra

Answer 19

that's what he's working from phi

Answer 20

What?

Answer 21

Another?

Answer 22

Sure

Answer 23

Well ill be damned.. it was right!

Answer 24

got one you want to post? or should I make one up?

Answer 25

wait, ill try the next one. 6x+3=2x+7

Answer 26

just go ahead and see how far you get

Answer 27

So i subtract 2x from both sides, getting 4x+3=7

Answer 28

good, then?

Answer 29

Then i subtract 3 from both sides, getting 4x=4

Answer 30

good, then?

Answer 31

And then i divide 4 by 4 and get 1 as the final answer :D

Answer 32

:D

Answer 33

well taught turing:)

Answer 34

TT, you are an awesome teacher!

Answer 35

tadah! nice
see how you didn't need to ask me which was better, subtract 7 or 3?
you knew by looking that 3 was the smart way to go :)
practice practice...
thanks for the compliment btw

Answer 36

So where do i go on from here?

Answer 37

have you done ALL the exercises from this section already?

Answer 38

Soon. you mean until i can choose another section right?

Answer 39

Yes.
It is imperative that you do every problem. This needs to become second nature for you
when you can look at
5x-3=2x+12
and tell me the answer very quickly, with almost no work shown, then you can continue

Answer 40

3/4?

Answer 41

actually 1/3

Answer 42

nope, better keep working on it.
practice practice...
don't try to get ahead of yourself, if you need to write it and go slowly, do it.
Don't try to shortcut past that.

Answer 43

alright. but i couldnt figure the last one out, it was 6x+6=0

Answer 44

I didnt know what to do there. was it 1 or 0? maybe -6?

Answer 45

just try the problem and show me your steps
you don't need to tell me what each step is, btw, I can see by looking

Answer 46

it was 9x+9=3x+3
6x+9=3
6x+6=0
6x= -6?

Answer 47

so now what is the last step to get x all alone?

Answer 48

tht was correct now show us your next and final step

Answer 49

6/-6?

Answer 50

perfect

Answer 51

now simplify that

Answer 52

-1?

Answer 53

correct

Answer 54

Yes!

Answer 55

yes, very good
what was the last step?
dividing by...?

Answer 56

that wasn't too bad now was it!

Answer 57

The number on the right?

Answer 58

dividing the quantity of x by the number on the right side of =?

Answer 59

Other*

Answer 60

no, that is what I was afraid of...
though you got the right answer, the -6 should have stayed on top.
6x=-6
what do we divide by to isolate x?

Answer 61

-6 with 6?

Answer 62

it's just one answer:
divide by 6

Answer 63

let's try something a little different...
solve
xy+7=10
for x

Answer 64

Ok

Answer 65

Note that above for
6x=-6
we divided both sides by the number next to the x (i.e. 6), that is what I wanted you to see. We do not divide by the number on the right. You will see why in this next problem

Answer 66

1.5 or 2 for x

Answer 67

Ok..

Answer 68

so now
xy+7=10
you got a number answer? what happened to y?
please show steps.

Answer 69

@turing does he know what he is solving for?

Answer 70

solve for x
thanks karate

Answer 71

anytime turing:)

Answer 72

I thought that x times y would be the answer. since 1.5x2 is 3 (which was needed to make 10) i thought that x would be 1.5 or 2.(the other one being y)

Answer 73

you are over-thinking Inopeki
just take each step one-by-one
what is the first step?

Answer 74

Determening what i need to make to complete 10

Answer 75

no
the first step is the same as the others
xy+7=10
subtract 7 from both sides

Answer 76

what do we have after?

Answer 77

Ah.. xy=3

Answer 78

good!
now again, we want x by itself.
it looks like x is being multiplied by y, so how can we get x by itself?

Answer 79

Removing y from the equation?

Answer 80

y cannot leave the equation entirely, we can only shift it to one side.
I mentioned that x was being multiplied by y. Do you know the inverse operation of multiplication?

Answer 81

division?

Answer 82

right!
and in this case what do we need to divide by to get x by itself?

Answer 83

y with 3?

Answer 84

close, but what do you mean "divide by y with 3"? that makes no sense
again it can only be one answer
divide by...?

Answer 85

just to make it visible again:
xy=3
what do we divide by on both sides (one answer to this question)

Answer 86

Ah, divide x and 3 by y?

Answer 87

YES!!!
and what do we have after?
write the expression.

Answer 88

How can i do that when i dont even know what y is?

Answer 89

Good question.
write the answer first and I will tell you what it means after.

Answer 90

You mean x/y=3/y?

Answer 91

close, but on the left x should be by itself, that's why we divided by y right?
so it should be...

Answer 92

I GET IT NOW! because the left side was x times y we needed to isolate x so we divided x with y to reverse the effect. now it is x=3/y

Answer 93

YES!!!
very good!
but what does it mean...?
as you said y can be any number (except zero, but we'll discuss that later)
so we have
x=3/y
that means we have infinite solutions to this problem. To find what they are plug in various numbers for y.
So what is x if
y=1
y=3
y=10
???

Answer 94

1.5?

Answer 95

no, its different for each one. Remember that I said there were infinite solutions. just plug in the numbers into the equation
there is no one answer for
x=3/y
so plug in a number for y like
y=1
what is x?

Answer 96

3

Answer 97

yes!
what about when y=3?

Answer 98

1