-2x-4=8x-6

In problems like this, we want to get x alone, or in other words, x = something.

We just have to manipulate this a little until we get that. The key thing to remember when changing things around is that whatever you do to one side, you have to do to the other side.

This is what we have:

 -2x-4=8x-6               ---Let's add 2x to both sides. This will "erase" the 2x from the left side.

+2x             +2x

------------------------

-4 = 8x +2x -6            

Now we can add the 8x and 2x together to get 10x. We can do this because any number times 8 + that same number times 2 = 10 times that number. To show you this, ill put in some numbers.

----------

8x+2x = 10x

8(2)+2(2)=10(2)

16+4=20

20 = 20

This a true statement, so it works. Let's try it with one more number.

8x+2x = 10x

8(9)+2(9) = 10(9)

72+18=90

90=90

Again, this is true, so we know we can do this next step I explained.

 ---------------------------

Let's do that step. 

-4 = 8x +2x -6  

-4 = 10x - 6              ---Now add 6 to both sides. The will "erase" the 6 from the right side.

+6          +6 

----------------

2 = 10x                ---We're almost there, now we just divide both sides by 10.

2/10 = x             ---Reduce the fraction on the left side.

1/5 = x

So...

x = 1/5

I see someone already answered. Hopefully my explanation can help too. :)

-2x - 4 = 8x - 6

Add 6 to both sides  

-2x +2 = 8x

Add 2x to both sides

2 = 10x

Divide both sides by 10

2/10 = x

or x = 2/10

or x = 0.2

Alan has provided an answer ND, and your answer was quite thorough.......very nice.....

Good, thorough explanation ND!

Thanks guys. I tried to explain it pretty well so our questioner could solve his other problems aswell.

There may be a little bit of unnecessary information. :)