Question

Solve the linear equation.

Answer 1

\[\frac{ x-6 }{ -3 } + \frac{ x+9 }{ 9 } = x + 4\]

Answer 2

assuming for x?

Answer 3

I don't remember whether to actually divide -6-3 or subtract them... or maybe it's -6+9

what do you mean o.o

Answer 4

you said solve the linear equation, then you posted one, I am assuming you mean to solve for x

Answer 5

I think so...

Answer 6

okay
how much information do you need? Do you know how to do any of it, or need all of it?

Answer 7

I think I just need to know how to start it off. Anytime I see fractions, my mind blanks e.e

Answer 8

okay, what you need to do is find a common denominator on the left side

Answer 9

like this

Answer 10

\[-3((x-6)/-3) =(-3x+18)/9\]

Answer 11

Then combine the numerators to get -3+18+x+9 which is -2x +27 all over 9

Answer 12

Then multiply both sides by 9 to get rid of the denominator

Answer 13

would you like me to keep going?

Answer 14

I'm a little confused...

Answer 15

\[-3(\frac{ x-6 }{ -3 })= \frac{ -3x+18 }{ 9 }\]

Answer 16

That is the first step, does that make sense?

Answer 17

\[\frac{ -3+18 }{ 9 }+ \frac{ x+9 }{ 9 }\]
\[\frac{ -3x+18+x+9 }{ 9 }=
\frac{ -3x+x+18+9 }{ 9}=
\frac{ -2x+27 }{ 9 }\]

Answer 18

does this make more sense?

Answer 19

what happened to the x+4 on the right side and how -3x+4 get to the right of the equal sign?

I understand how you did the second problem but for some reason I'm not understanding the same steps in the original problem >.<

Answer 20

the steps I just did are from the problem you gave. I was only working with the left side, I can do that because all I did was multiply by 1 and rewrote it. I don't know where you got -3x+4.

Answer 21

o.o I meant x+4 that was on the RHS
and that second problem was the next step from the actual problem that you just did? e.e oh my goodness
so sorry I'm a little slow lol

Answer 22

So do you understand what I was doing? I can reexplain it if you want?

Answer 23

I understand every step except for how you knew how to get the second step (where you place the -3 in a distributive position)

Answer 24

I know you needed a common denominator but I mean...like...where does that 3 even come from

Answer 25

That should be \[\frac{ -3 }{ -3 }\] I meant to do that. The reason I knew to use the -3 is because -3 is a factor of 9 so I wanted to get 9 as my common denominator, so since -3 *-3 is 9 i multiplied -3 by the top and bottom of the first fraction on the LHS. Does that make sense?

Answer 26

so if the equation looked like
\[\frac{ x-4 }{ -2 } + \frac{ x-8 }{ 4 } = x - 6\]

and you needed a common denominator, you'd
\[-2(\frac{ x -4 }{ -2 }) +\frac{ x-8 }{ 4 } = x-6\]

Answer 27

or no...?

Answer 28

yes, except it should be \[\frac{ -2 }{ -2 }\] so you are multiplying by 1 and not changing the problem but rather changing the appearance. That was a notation mistake on my part.

Answer 29

oooh I think I get it now

Answer 30

Would you like for me to keep going?

Answer 31

Yes please, if you don't mind.

Answer 32

Not at all, I live for this, literally I am a math teacher.

Answer 33

Lol, glad to hear and I appreciate your time and effort. Thank you.

Answer 34

So now you multiply both sides by 9 to get rid of the denominators. \[9(\frac{ -2x+27 }{ 9 })=9(x+4)\] the 9s on the LHS will cancel out so you will be left with \[-2x+27=9(x+4)\]

Answer 35

Your welcome

Answer 36

Would you like for me to continue?

Answer 37

Yes please

Answer 38

now you distribute to get, \[-2x+27=9x+36\]

Answer 39

Then you get to pick one of the terms, any of them. Which one do you want to use?

Answer 40

o.o um... 9x?

Answer 41

okay so now you move 9x by subtracting it since it is positive, by the way, this will work with any term you choose.
\[-2x-9x+27=36\]

Answer 42

Now you add like terms:
\[-11x+27=36\]

Answer 43

Then you move the +27 since you need to get the variable by itself\[-11x+27-27=36-27\]
\[-11x=9\]

Answer 44

Then divide both sides by -11 and you will get our answer

Answer 45

so basically \[x = -\frac{ 9 }{ 11 }\]

Answer 46

Should be

Answer 47

Thank you very much c:

Answer 48

Your very welcome