algebraic equations!! help with maths?

3x-21= x+5

okay, the technique here is to combine similar terms.

so,

3x-x= 21+5

note that as you transfer the number to the other side, its positive/negative value changes. If it is negative, it turns positive. If it is positive, it turns negative.

Then, you do the basic operations:

3x-x= 21 + 5
2x= 26

Then, you've got to divide both sides by 2:

2x/2= 26/2

x= 13

then that's it!

There are quite a few answers here already, so I hope I won't simply be repeating them! I don't teach the balance method but I will show you how to:-
I like to think of the numbers being glued to the x's or y's. Some are glued more firmly than others so for example the -21 is glued less well than the 3 in the 3x. I get rid of the ones that are not glued so well first of all.

To get rid of anything, you do the opposite to what got it there!
The -21 for example was taken away from the x bit so.... add it back on to the left hand side. [The balance method relies on you undoing what was done to x] Because it has to be even, if you added 21 to the l.h.s [ left hand side] you must also add it to the r.h.s [right hand side]

Now you have
3x -21 +21 = x +5 +21

work out the bits of the sum that you can
this makes

3x = x +26

Your aim is to have only x's on the l.h.s
That means that you have to get rid of the x on the r.h.s
It is +x so to get rid of it you do the opposite which is -x. Don't forget, because it is an = you have to do the same to the l.h.s

This means your equation now looks like this:-

3x -x = x - x +26

Now working that out makes

2x = 26

Now to get rid of the 2 on the l.h.s
It is multiplying the x [ 2x means 2 times x]
so to undo it you have to divide by 2. Doing it to both sides to keep it balanced...
2x/2 =26/2

working that out you get

x =13

Hope that is all crystal clear !! lol I haven't shown you the way that I normally teach it because I don't want to confuse you. If you wish me to just ask

3x - 21 = x + 5
3x - x = 21 + 5
x = 26/2
x = 13

Here are the rules I used to give my students.

1. Simplify both sides by removing parentheses then combining like terms. You don't need to do this in your example.

2. If there is a variable on both sides, eliminate one by adding its opposite to both sides. I used to tell them to get rid of the one on teh right, but it makes no difference.
3x-21=x+5
3x -x -21=x-x +5
2x-21=5
3. Eliminate the constant with the variable term by adding its opposite to both sides.
2x-21=5
2x-21+21=5 +21
2x=26
4. Eliminate the coefficient of the variable by dividing both sides by it or multiplying both sides by its reciprocal (good to know if the constant is a fraction).
2x=26
2x/2=26/2
x=13

In balancing scale terms, x is your box of unknown mass. In an equation like this, you have 3 boxes of the same unknown mass on one side, and one on the other. So you can take one box off each side, leaving two x boxes on the left and none on the right (as well as the other numbers). Algebraically:
3x - 21 = x + 5
3x - 21 - x = x + 5 - x
(3x - x) - 21 = (x - x) + 5
2x - 21 = 0 + 5 = 5

Then, to get rid of the -21 on the left so there's only x's on that side, you have to subtract -21 from both sides - which is the same as adding +21.
2x - 21 = 5
2x - 21 + 21 = 5 + 21
2x = 26

Finally, you've got two x's on the left, and a known weight of 26 on the right. Halve both sides for the last step.
2x = 26
2x / 2 = 26 / 2
x = 13

Just remember these rules when trying to solve this kind of equation:
1) Anything you do to one side (adding something, multiplying by something, etc.) you *must* do to the other.
2) To start with, try to get all of the unknown stuff on one side, and all the known stuff on the other. To do that, subtract them off the sides they shouldn't be.
3) One you've done that, you'll usually have *some number* of unknown on the left. Divide by *some number* so that you only have one of them.

3x-21=x+5
First subtract x from both sides of the equation and combine like terms.
3x-21-x = x-x+5
2x-21 = 5
Then add 21 to both sides.
2x-21+21 = 5 + 21
2x = 26
Divide both sides by 2.
x = 13

3x-21=x+5
2x-21=5 (minus x from both sides of the equation)
2x=26 (add 21 to both sides of the equation)
x=13 (divide by 2 on both sides of the equation

Therefore, x = 13

3x-21=x+5
3x-x=5+21
2x=26
x=13 answer//

checking

3(13)-21=13+5
39-21=18
18=18 correct!

3x-21=x+5
3x-x=5+21
2x=26
x=13

x= 13