Question

how does 3+2(-11/14) become 3-11/7?

Answer 1

14 is cancelled by table 2 as 2*7=14

Answer 2

According to PEMDAS, the order in which you do operations is such:
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Since you have multiplication in the problem, you would do the multiplication before the addition.
3 + 2 x (-11/14)
The 2 cancels part of the 14 because it is factorable by 2:
2 x -11/(2 x 7) = -11/7
Since the 3 is unaffected by the multiplication, it remains in the equation.

Answer 3

I think I understand.

Answer 4

thats gud.

Answer 5

so how would you proceed to the next step? x=(3-11/7)-2z.......How do you solve 3-11/7

Answer 6

to solve 3-11/7
taking L.C.M,
=(21-11)/7
=11/7

Answer 7

sory its 10/7

Answer 8

l.c.m?

Answer 9

so does 3-11/7 become 3/1*11/7 and cross multiply 3and 7, 1 and 11?

Answer 10

but then wouldn't the answer be 3?

Answer 11

yes l.c.m

Answer 12

l.c.m is of the numbers in denominatot

Answer 13

3/1-11/7 so we have 1 and 7 in denominator so 7 is the l.c.m

Answer 14

no its not cross multiplication i just took l.c.m

Answer 15

l.c.m stands for "Least Common Multiple," but you can call it the least common denominator too. To add 3 to 11/7, you need to make sure that the denominators are the same.
So yes, 3 is currently divided by 1, and 11 is divided by 7. You can't cross multiply for this part though because the numbers are not in a proportion.
So to make the denominator on 3 equal to the denominator under 11, you would need to multiply it by 7.
So 3/1 x 7/7= 21/7

Answer 16

I'm sorry, I don't even understand what LCM is, I haven't done math in 15 years

Answer 17

i got it what are u sayng,its ok in ur sense cross multiply after l.c.m

Answer 18

ok dnt worry i tell what the l.c.m is

Answer 19

so then it becomes 21/7-11/7?

Answer 20

and then 10/7 okay!

Answer 21

Yup! That's it!

Answer 22

so now what is the next step, x=10/7-2z

Answer 23

as on present case we have 1,7 so
we divide both on a single number until we get 1 then multiply those numbers which is l.c.m

Answer 24

Are you solving for z?

Answer 25

ok its 2z?solving 4 z or x?

Answer 26

ummmm, this was the original equation,
4x+6y-8z=1
-6x-9y+12z=0
x-2y-2z=3

Answer 27

Ohh. You're supposed to solve for all of the variables, right?

Answer 28

ok u have system of linear equations to solve

Answer 29

yes, w/ help I got this far,
x=3-2y-2z
4(3-2y-2z)+6y-8z=1
-6(3-2y-2z)-9y+12z=0
and then
4(3-2y-2z)+6y-8z=1
12+8y+8z+6y-8z=1
12+14y=1
14y=-11
y=-11/14
so
x=3+2(-11/14)-2z
x=(3-11/7)-2z
and so now I'm at x=10/7-2z

Answer 30

so now I know y=10/7 or 1 3/7?

Answer 31

Wow..that looks like a lot to type. Hmm, ok.
There's a small error in the beginning. The third equation you wrote was x-2y-2z=3, right? In the last post you made, you replaced x with 3-2y-2z. Those equations are actually not equal, but it's just a problem with positive and negative signs.
x-2y-2z=3
Since you want x separated from the other two variables, you would move them to the other side of the equation. First, you would add 2y to both sides to keep the equation balanced (remember, what you do to one side of an equation must be done to the other, just like a seesaw).
So add 2y and 2z to both sides to separate x.
x=3+2y+2z

Answer 32

okay, so then it becomes 4(3+2y+2z) +6y-8z=1
12+8y+8z+6y-8z=1
12+14y=1.....so it still comes out the same in the end doesn't it? Am I not still left with x=10/7-2z?

Answer 33

OOO no, it changes it to x=10/7+2z

Answer 34

Whoa, you lost me xD
Well from there you can get y, which is still correct. And if you plug y into that equation, it becomes
x=3+2(-11/14)+2z
So yes, the last one you posted was right.

Answer 35

okay, so how do I solve it? how do I solve x=10/7+2z?

Answer 36

do I now know that y=10/7? how do I figure out x and z?

Answer 37

Okay, so far you've only had to use two equations. You can plug in the new x value (10/7 + 2z) into the last equation to solve for z since you already know that y is equal to -11/14.
The y you got from the 12+14y=1 that you solved earlier. So you already know what y is!

Answer 38

so now the equation is -6(10/7+2z)-9(10/7)+12z=0?

Answer 39

Err...yes to everything except the 10/7. The equation for y you had earlier was
12+14y=1
When you solved for it, you ended up with -11/14.

Answer 40

oh....ok so 10/7 only works in the x-2y-2z=3 equation?

Answer 41

or the 4x+6y-8z=1 equation?

Answer 42

I thought I was getting it, but now I'm confused all over again

Answer 43

The 10/7 you got in that equation wasn't equal to any of the variables, actually. It was just part of the equation for x. The equation was x=10/7 + 2z, right? All the 10/7 tells you is that x is 10/7 larger than twice of z. It doesn't stand for a variable.

xD Math is such a joy, isn't it?

Answer 44

lol yea

Answer 45

okay. so y=-11/14

Answer 46

so now I do x=2(-11/7)+2z?

Answer 47

or 4(3+2(-11/7)+2z)+6(-11/14)-8z=1 and -6(3+2(-11/14)+2z)-9(-11/14)+12z=0?

Answer 48

becoming 12+8(-11/14)+6(-11/14)+4z=1and -18-12(-11/14)-9(-11/14)=0

Answer 49

Whoops, sorry. I had to go find the equations again.
Whoaaah. You could do that, but trying to keep your variables straight gets really confusing, doesn't it?
When it comes to multiple equations like this, it's usually easier to try and separate a variable before putting in more values. So instead of plugging in the values for x and y in the beginning, try separating x or z from one of the equations first.
Say we took 4x+6y-8z=1
We could pull out the z to make it a little less confusing.
So 4x+6y=1+8z
4x+6y-1=8z
And you could divide both sides by 8 if you really wanted to, but it depends on how comfortable you are with fractions...and on a computer screen, fractions are hard to keep track of.
Then for y you would plug in -11/14

Answer 50

I'm good with fractions for the most part, it's the rest of this junk

Answer 51

and I'm keeping track on paper too :0)

Answer 52

so it would become 4x+6(-11/14) -1=8z?

Answer 53

And for x, you could plug in either the original equation of
x=3+2y+2z or the simpler x=10/7+2z that you figured out earlier.

Oh, then you shouldn't have any problems xD I think I'm avoiding fractions for myself, just because I never see the division sign...

Answer 54

Yup. It has a lot less numbers than before, right? xD

Answer 55

okay....so 4(10/7+2z) +6(-11/14)-1=8z

Answer 56

yea it does

Answer 57

okay, so I figured the first half, 40+8z, how do you multiple a positive with a negative?6(-11/14)

Answer 58

To multiply a negative number, the rules are pretty simple. If you multiply a negative by a positive (as in this case), the result will be a negative number. It multiplies the same as two positives though. If you have two negative numbers, then the result will be positive instead.

Answer 59

aha, so then 6(-11/14) becomes -66

Answer 60

so then the equation becomes 2z-27=8z

Answer 61

Yep, but don't forget to divide by the 14.
OH NO. I'm sorry, I wasn't paying attention to the equation I picked! We already used this equation to solve for the x value, so the variables are just going to cancel out...You have to use the third equation to solve for z.
So use -6x-9y+12z=0...
Ahh...my bad.

Answer 62

oh okay, hold on. let me try

Answer 63

okay, so:
-6x-9y+12z=0
-6x-9y=-12z
-6(10/7)+2z)-9(-11/14)=-12z
-60+2z+99=-12z
39+2z=-12z
39=-12z-2z
39=-14z?

Answer 64

so z=2 -11/14

Answer 65

or more like -2 11/14

Answer 66

Ahh...almost. You have the equation right, but somewhere in the middle of multiplying you dropped your denominators.
Take 6[(10/7)+2z], for example.
When you multiply by the 6, you should end up with (60/7)+12z, rather than 60+12z.

Answer 67

ummmm....6(10/7) ooooohhh okay

Answer 68

Mmhmm. The same goes for the -9(-11/14). You got the positive sign right on that part though :D

Answer 69

okay, i'll try again

Answer 70

so -6 is a whole number, so to multiply it by 10/7 you have to make it a fraction correct? so it becomes -6/1x10/7. then you have to have common denominators and what you do to the bottom you do to the top? -42/7x10/7 then becomes -420/7 becoming -60?

Answer 71

or was that other person wrong, and it's just -6/1x10/7=-60/7?

Answer 72

-8 4/7(simplified)

Answer 73

The least common denominator is really only used when adding and subtracting. So the other person was right on that part. For multiplication, the last thing you posted is correct.
I'd be careful with mixed fractions (the whole number with the fraction) only because multiplying them gets tricky.
And...I think something went wrong again because my variable disappeared. Let me try doing the problem on paper ^-^'

Answer 74

okay, i'm working it out on paper too, and this is where i'm at,
-60/7+2z-99/14=-12z
-219/14+2z=-12z
-219/14=-12z-2z
-219/14=-14z

Answer 75

so now I divide -219/14 by -14 to =z?

Answer 76

-219/14 divided by-14/1=-219/14x-1/14=219/196

Answer 77

There's one more thing missing in your multiplication. When you multiply something inside of parenthesis, you have to multiply everything inside.
So you had 6[(10/7)+2z], right? You have to multiply both the 10/7 AND the 2z by 6 because they're inside the parenthesis. It goes back to the PEMDAS thing I mentioned a long time ago.

Answer 78

crap. I thought I did that.

Answer 79

okay so -60/7-12z+99/14=-12z

Answer 80

therefore, -3/2-12z=-12z

Answer 81

Yup, that's what I've been getting. But from there, the z keep getting dropped, no matter which equation I use..

Answer 82

-3/2=-12z+12z

Answer 83

yea, it did it for me too, so does that mean there is no solution? we find out x and y but never z?

Answer 84

Technically, you can find z if you find x. But we shouldn't be dropping z in every equation we try because...well, it's not really logical, I guess. I'm still looking to see if I messed up too.

Answer 85

okay

Answer 86

Ahh, no good. I'm running in circles now. Are you sure the original equations are right?

Answer 87

That's what I was given. :0( Well thank you for all your help, I think it's time to call it a night. I will have to double check the equation tomorrow, and try again if the originals were wrong. Thank you for your patience, at least I know how to figure it out next time!

Answer 88

Okay then. Sorry I couldn't help more though!

Answer 89

It's okay, you were great! Thank you!

Answer 90

No problem! Good luck tomorrow!