Long/two variable equations

Again, I'm not supposed to be here, but desperate times call for desperate measures...

I stink at Math. I'll say that flat out, I stink at math, and tonight on my homework, I basically skipped more than 75% of the questions because I just can't figure them out. I have no clue why, I used to be good with equations, but these ones are just killing me. And I'm not exactly doing spectacular in math, so I wanna try and build up my grades. If I get this trouble down, I'll have made some progress

What I'm having a problem with are long-term equations that have the double variables, here's a couple directly from my homework for example-


18= -6x + 4(2x + 3)


10z - (3z- 11) = 17


Now, equations that have only one variable I'm perfect with, these just kill me though. If anyone can help me, just explain or give me a rundown of how to figure these out without me spending 10 minutes per problem doing random ideas off the top of my head for the number, I'd greatly appreciate it. You'll be helping me more than it may seem.

It's easy, just combine like terms.

18 = -6x + 4(2x + 3)

Now the Distributive Property..

18 = -6x + 8 x + 12

Now combine the like terms..

2x +12 = 18

Subtract the 12 from both sides..

x = 3

It's really simple once you get the hang out it, now try the second one out again.

A more complete explanation:

Distributive property basically means that if you have something like
2(2x+1), you can multiply both things inside by 2, and it will still be the same thing, so, 2*2x+2*1 = 4x+2

Something like -(3z-11) could also be written as -1(3z-11), so would be -1*3z - -1*11 = -3z + 11. Remember that multiplying two negatives equals a positive, and a subtraction problem can be written as an addition problem, so, 3z - 11 = 3z + -11

First one.

18 = -6x + 4(2x + 3) becomes:

18 = -6x + 8x + 12 by multiplying (2x + 3) by 4. That takes us to:

18 = 2x + 12 by putting -6x and 8x together. Next:

6 = 2x by taking 12 away from both sides. Divide 6 by 2 to get x, so:

x = 3.


Second one:

10z - (3z -11) = 17. First, forget about the parentheses and just put 10z and what is now -3z together to get:

7z - 11 = 17. Add 11 to both sides to get:

7z = 28. Divide 28 by 7 to get z. After doing that, we find that:

z = 4.


So, you comprehend this? These really were just one variable equations as well.

Mirren, buddy, I had problems with this myself, but I got over it. Here's an easy way:

18= -6x + 4(2x + 3)

First things first, distributvie property:
18=-6x+8x+12

Now, combine the like terms(which is 6x and 8x):
18=2x+12
Remember, -6 needs to be subtracted by +2 to get the anwser, which is +2 due to the smaller number being a negitive

Ok, fun time. Start by subtracting 12 and eliminating the 12-12 problme, by crossing it out. The subtract 18 minus 12:
6=2x
Now divide 2 by 2x and 6. Cross out 2x divided by 2 and then do 6/2
3=x
There, easy

I could help you on the 2nd, but I think the others did that for ya.

Well, there is a difference between a two variable equation and what you gave us...
to be precise a two variable equation, would invovle two different variables...

for example y= log x 1
or a= 2b+32
or 3n+5z=2

these are solved in a vary different matter and require either a supplemental equation or else they must be graphed. What you are doing is a one variable equation, there is only one type of variable in your case X and then Z. DO not confuse this with a quadratic equation (which includes X^2 or X*X if (that makes more sense, ZU will not allow the proper formatting for this problem) and posibly another variable if it is to be graphed or merely X^2s, Xs, and constants if it is to be solved)

in genereal what you will want to do for this is the opperations within the following:
P-parenthanses
E-Exponents(in cludes square roots which are technically exponents)
M-multiplication (include multiplication of fractions which is division)
A-Addition(includes addition of a negative number which is equivillent to subtraction)

if you cannot remember that try the dumbell acronym which is less proper is: PEMDAS which is Parenthesis, exponents, multiplication, division, addition, subtraction. I used this from 4th through 7th grades so its nothing to bad...


so do the order of opperations from left to right (PEMDAS), then group like terms (say X+5X which would be 6X) then simplify further if needed. then work on both sides of the equation with the properties of equation to get your end result.
I am assuming that you are an either grader in Pre-Alebra, I am more than willing and capable to help you over AIM if you ever need it(this applies to everyone who needs help all the way up to precalculus or trigonometry) I may not be able to help for all the things in pre-algebra though because I was placed in thewrong math class in 6th grade, I was supposed to take pre-algebra(or perhaps even Algebra, I did not know the proper class because I was in gifted classes(G.A.T.E.) and then transfered to another school district that did not have them for my grade level so I was unsure as to my exact placement) in 6th grade but insteed I did not so I skipped it and in 7th grade I went strait to Algebra.

Unlike you, I did not suck at math until algebra II(maybe because we had a teacher that never collected homework, so I did virtrually none...) but I still manage to ACE math with a cool A-.

EDIT: DIUM, I was clarifying somethings, do not feal that stating this is worth a post, I may be a post whore but not that big of one...

Originally Posted by zelink

to be precise a two variable equation, would invovle two different variables...

for example y= log x 1
or a= 2b+32
or 3n+5z

That is what I thought he meant... untill I read his post.

You really should get into the habit of combining every like term, and then getting all variables on one side of the equation and all other numbers on the other. Believe me, it may seem pointless in some of the easy equations now, but once you get into more and more complex stuff, it helps a TON to be used to doing it by default. I learned this the hard way, and once I started quadratics I DIED.

Well... maybe that was because I never did any homework. But you know. Either one. I'm just reinforcing facts already said, so ignore me if you must...

IN OTHER NEWS... Live through Algebra One and you get to Geometry (usually). Which is friggen easy. Relatively speaking. And Algebra 2 aint that bad either. So cheer up! It's all good.