question on solving linear equations?

[thepcnerd]

question on solving linear equations?

when u are collecting like terms, for instance on problem

-3y+3y+8=4y+3y-6 the -3 thats now a +3 do u only xfer the number or variable if its the smaller one, such as if its onthe left as it is here i xfer it to the right?

on this prob its on the left, so we xfer the smaller number/variable to the left?

6-10u+7u=-7u+7u+24

from what i can understand i would take the smaller number/variable on the collecting terms and move it over to the opposite side changing the -, + where applacable right?

pls help asap as im studying for my intrance college exam thanks

 

[jonboy]

Hi, thepcnerd!

From what i can understand i would take the smaller number/variable on the collecting terms and move it over to the opposite side changing the -, + where applicable right?

Do not think of it like that. Think of this process as subtracting/adding a number (any number/term) from both sides of the equation, keeping the equation still balanced.

For instance, you second problem you posted: \(\displaystyle \L \;6\,-\,10u\,+\,7u\,=\,-7u\,+\,7u\,+\,24\)

Collect like terms: \(\displaystyle \L \;\,-3u\,+\,6\,=\,24\)

Subtract \(\displaystyle 6\) from both sides of the equation:\(\displaystyle \L \;-3u\,=\,18\)

Divide both sides by \(\displaystyle \,-3\):\(\displaystyle \L \;u\,=\,-6\)

 

[thepcnerd]

ok

but what im trying to understnad is how do i know when im going to combine like terms form the left ot the right or right to the left, how do u know when each problem can be done, as with the 2nd problem i wrote if u were to move the -10 oer andake it a +3 all the math can be done the same and i would get a +3 but im supposed to get a -3, this is what i dont understand how do u justify when and why u some times move numbers to the left or to the right, does nt make any since,

 

[stapel]

but what im trying to understnad is how do i know when im going to combine like terms form the left ot the right or right to the left, how do u know when each problem can be done, as with the 2nd problem i wrote if u were to move the -10 oer andake it a +3 all the math can be done the same and i would get a +3 but im supposed to get a -3, this is what i dont understand how do u justify when and why u some times move numbers to the left or to the right, does nt make any since,

Um... what? :shock:

I'm sorry, but your post is almost entirely unintelligible. Using punctuation, capitalization, and correct spelling would go a long way toward letting people know what you're trying to say.

There is no one sacred "right way" to proceed with solving linear equations. A good first step is to combine like terms on each side of the equation, but this is a good starting step not because it is required, but because it makes your work easier by simplifying what you're looking at. Then a good next step would be to move all the terms containing variables to one side of the equation, and move all the terms containing no variables to the other side. This is a good next step because it lets you further simplify. There is no one "required" side on which the variables "must" go; it's your choice. Then you would combine the terms on either side of the equation, and, if necessary, divide through to solve.

It's a general process that you need to learn, not a rigid list of rules.

Eliz.

 

[thepcnerd]

sry im at work and we get busy and slow, so i have to type fast...

what im asking is how do i know when i move numbers/varaibles to the left, ive always been taught to move all variables to the right

 

[stapel]

sry im at work and we get busy and slow, so i have to type fast.

It really doesn't take that long to hit the "Shift" button.... :roll:

[W]hat [I'm] asking is how [I would] know when [to] move numbers/[variables] to the left[. I've] always been taught to move all variables to the right[.]

As mentioned previously, the side to which you move the variables is irrelevant. You can always switch sides later.

Eliz.

 

[pka]

how do i know when i move numbers/variables to the left, I have always been taught to move all variables to the right

I certainly hope that you have not been taught any such idea!
First of all, one can only ‘move’ something that one can pick up.
I have never seen anyone who can pickup a number in an equation.
Now, it is any equation with two sides of the equal sign.
We can add or subtract any number or variable on both sides.
We can multiply and divide.
The idea is to end up with variable equal to some quantity.
This is an example of that:
\(\displaystyle \begin{array}{rcl}
3t - 6 & = & 6(2 + t) \\
3t - 6 & = & 12 + 6t \\
- 6 & = & 12 + 3t \\
- 18 & = & 3t \\
- 6 & = & t \\
\end{array}.\)

 

[thepcnerd]

k

thanks makes since now.... sry bout my attitued earlier.