Help needed! Anyone good at algebra??

[BFG]

I think you'd be best finding a website that takes you through the basics.

Basically you're simplifying the equation where possible. So 1A(pples) + 3O(ranges) + 12A(pples) - 1O(Oranges) = 13A(pples) + 2O(ranges)

So, from the example above, find the things that are the same and combine them.

3x^2 + 3x + 5x^2 + 6x =

3x + 6x is the same as 9x and 3x squared + 5x squared is the same as 8x squared.

8x^2 + 9x =

This step is a bit trickier. Both parts are being multiplied by x, so you can divide both of them by x to cancel it out/get rid of it.

8x + 9

I have to admit, I find the one sided equation a tad confusing. It's easy to understand with something like

10A(pples) = 100p(ence). You've got 10A, so to simplify it, you divide both side by 10 (the opposite of multiplying by 10).

So 1A = 10p.

Er... Not sure I've helped any. Find a good website!

[elsie-scot]

OK I dont get what others get, what age of maths did you say this was?

3xsquared + 3x + 5xsquared + 6x =

9x+3x+25x+6x = 50x

[pipscariad]

OK I dont get what others get, what age of maths did you say this was?

3xsquared + 3x + 5xsquared + 6x =

9x+3x+25x+6x = 50x

Do you mean as in what level is it aimed at? My boys are 12, in year 8, so still fairly basic(ish) stuff. I could really do to teleport some of you into my kitchen, and do it first hand! Elsie, I see that you have dealt with the squared numbers by timesing (is that a word?! Hopefully you know what I mean!) them by themselves, which is what I thought I needed to do. I can understand your answer (but don't really 'get' the others, sorry Nerobot and BFG ), but as you say, it's not the same as the others. Oh, grrrrr.....

BFG, I know I should have found a website, it's just that there were so many, and you Grapes are so approachable and friendly . Plus I felt I needed to be shown how to do it with one of the actual questions.... but maybe that's just me being odd!

[nerobot]

pipscariad:

3x^2 + 3x + 5x^2 + 6x =

(3+5)x^2 + (3+6)x =

8x^2 + 9x =

There is an "x" in both parts, therefore:

x (8x + 9) =

Now, assuming, the initial equation is actually 3x^2 + 3x + 5x^2 + 6x = 0,
then

x (8x + 9) = 0

Then divide both sides by x to give:

8x + 9 = 0

Incase anyone isn't sure, x^2 = x*x

Another - longer - way would be to calculate it like this:

3x^2 + 3x + 5x^2 + 6x =

3*x*x + 3*x + 5*x*x + 6*x = 0

Divide everything by x to give

3*x + 3 + 5*x + 6 = 0 (since 0 divided by anything is 0)

Then simplify as per previous examples:

(3+5)*x + (3+6) = 0

=> 8x + 9 = 0
----------------------



HotStuff: First is correct, but what is the complex root of the second equation..........

Steven

[HotStuff]

OK I dont get what others get, what age of maths did you say this was?

3xsquared + 3x + 5xsquared + 6x =

9x+3x+25x+6x = 50x

The problem here is that "3 times x squared" is not the same as "3 squared times x"

In the equation above 3xsquared means "3 times x squared", so you take the value of x, times that by itself and then multiply the result by 3. For example if x had a value of 4, then 3xsquared means 3 times 4 times 4 = 48, whereas 3squared times x means 3 times 3 times 4 = 36.

In the algebraic equation above we don't know the value of x, but we do know that most of the time x will not have the same value as xsquared, so while we can gather together quantities of x with other quantities of x and quantities of xsquared with other quantities of xsquared we can't mix the two. So

3xsquared + 3x + 5xsquared + 6x

can be rewritten as

3xsquared + 5xsquared + 3x + 6x

all we've done here is changed the order of the terms to group them together, then as we know we can add together quantites of the same order we can rewrite the equation as:

8xsquared + 9x

[organic]

Just to clarify one part of what HotStuff just said...

The two ways of explaining 3x² might not be obvious to some so here we go.

I'll break them down another way to make it as obvious as possible.

When you see brackets in an equasion or expression (an expression is an "equasion" without an equals sign) you do that bit FIRST.
When you see 3x² you are actually doing 3(x²)
So it's x² times 3

If you're meant to do it the other way around it would be written as (3x)²
In that case you'd do 3 times x and then square the result.

Hope this helps.

[elsie-scot]

Do you mean as in what level is it aimed at? My boys are 12, in year 8, so still fairly basic(ish) stuff. I could really do to teleport some of you into my kitchen, and do it first hand! Elsie, I see that you have dealt with the squared numbers by timesing (is that a word?! Hopefully you know what I mean!) them by themselves, which is what I thought I needed to do. I can understand your answer (but don't really 'get' the others, sorry Nerobot and BFG ), but as you say, it's not the same as the others. Oh, grrrrr.....

BFG, I know I should have found a website, it's just that there were so many, and you Grapes are so approachable and friendly . Plus I felt I needed to be shown how to do it with one of the actual questions.... but maybe that's just me being odd!

Ok now I am muddled! Find it hard to believe that maths for 12 year olds is as complicated as the others worked it out as, but it has been a few years since I have done any algebra, can't really comment further. Good luck is all I can say!

[elsie-scot]

Just to clarify one part of what HotStuff just said...

The two ways of explaining 3x² might not be obvious to some so here we go.

I'll break them down another way to make it as obvious as possible.

When you see brackets in an equasion or expression (an expression is an "equasion" without an equals sign) you do that bit FIRST.
When you see 3x² you are actually doing 3(x²)
So it's x² times 3

If you're meant to do it the other way around it would be written as (3x)²
In that case you'd do 3 times x and then square the result.

Hope this helps.

This is easier to understand!

[organic]

I said in the "snow" thread that I'm half English and half Irish - the Irish half is a teacher!

Just to clarify the clarification...
The reason you don't see brackets when you're doing 3x² is because certain things are assumed. It's the same reason there's no multiplication sign.

The beackets around x² are assumed, just like the multiplication sign between 3 and x² is assumed.

If we wanted to be absolutely explicit about it we'd write this (x means multiply here, x is the letter)

3x(x²)

Since the x and the ( ) are assumed it's just written as 3x²

Any change from that and brackets will be included so you know it's to be handled differently.

[Bigmallly]

Sorry guys but I'm still at the starting gate.......shouldn't there be a number after the = sign so that you can work out the value of x. Or would that be just too easy.

[organic]

Mally - sometimes. Sometimes not.

I don't think any of the things pipscariad are actually "equations". The one that said "... = Ah!" was, I think saying that her response to the expression was "Ah!" not that there's an equals sign in the problem.
If it's not an equation then there's no way of calculating an unknown value (x in this case) because you don't know the result of the equation.

In simple terms: If I write this...
2+a
there's no way of knowing what a is.
If on the other hand I write this...
2+a=5
It's simple to figure out the value of a. To do so you just need to get a on its own. In this case you subtract 2 from each side and it gives you your answer. a=3.
The same principles apply with the questions above - I'll not go through the whole things but take, for example:

If there's an expression (no equals sign) that goes.
6a + 3x² -6a
Then the 6a and -6a cancel eachother out so you're left with 3x² and that's as far as you go. That's the answer.

If it was written as an equation (that is, with an "=" sign) like this though:
6a + 3x² -6a = 12
You'd reduce it down first (6a and -6a cancel eachother again) and get this.
3x² = 12
The next step is to divide each side by 3 which gives...
x² = 4
x = √4 (square root of 4)
x = 2

In that case you can "solve for x" but otherwise it's not necessary to go all the way to a numerical answer.
Sometimes (and certainly in this case) the way you handle the algebra is the important part, not the value of one of the letters.

Clear as mud? Or did that help?

[Bigmallly]

It certainly did.........it was the = that threw me.

[organic]

Brill!
Now...

1/√((3x²)³)=13.2
Solve for x.

As they used to say on The Big Breakfast "Don't phone! It's just for fun!"

I've got no clue what the answer is and have no intention of figuring it out - so even if you got it right I wouldn't know! It made for a decent gag though.

[HotStuff]

If it was written as an equation (that is, with an "=" sign) like this though:
6a + 3x² -6a = 12
You'd reduce it down first (6a and -6a cancel eachother again) and get this.
3x² = 12
The next step is to divide each side by 3 which gives...
x² = 4
x = √4 (square root of 4)
x = 2

or x = -2

[organic]

or x = -2

*slaps forehead*
OOPS!

It's been so long since I've even thought about quadratics I'd forgotten all about the other side of the curve! You are, of course, absolutely right.

Top of the class, gold star, yada, yada.