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how do you know which number to add to each side

Simplifying
6x + -2 + 2x = -2 + 4x + 8

Reorder the terms:
-2 + 6x + 2x = -2 + 4x + 8

Combine like terms: 6x + 2x = 8x
-2 + 8x = -2 + 4x + 8

Reorder the terms:
-2 + 8x = -2 + 8 + 4x

Combine like terms: -2 + 8 = 6
-2 + 8x = 6 + 4x

Solving
-2 + 8x = 6 + 4x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

((((((*******Add '-4x' to each side of the equation.*******))))))
-2 + 8x + -4x = 6 + 4x + -4x

Combine like terms: 8x + -4x = 4x
-2 + 4x = 6 + 4x + -4x

Combine like terms: 4x + -4x = 0
-2 + 4x = 6 + 0
-2 + 4x = 6

(((((****Add '2' to each side of the equation.*****)))))
-2 + 2 + 4x = 6 + 2

Combine like terms: -2 + 2 = 0
0 + 4x = 6 + 2
4x = 6 + 2

Combine like terms: 6 + 2 = 8
4x = 8

Divide each side by '4'.
x = 2

Simplifying
x = 2

THIS IS THE PROBLEM STEP BY STEP BUT HOW DO I KNOW WHICH NUMBER TO ADD TO EACH SIDE. HERE WE ADD THE -4X AND THEN THE 2.

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4 Answers

The order in which you add/subtract terms is not really important. Just make sure that what you do to one side, you do to both. You're goal is to get all the variables on one side and all of the numbers (constants) on the other. If you had added the 2 first and then dealt with the -4x, you would have gotten the same answer. 

Comments

ok but how do I know which number to add to both sides. (like why the -4x and not the 8x?) in this case ((((((*******Add '-4x' to each side of the equation.*******))))))
-2 + 8x + -4x = 6 + 4x + -4x

It doesn't matter. You can move the 8x to the other side, and you will find that you will still get the same answer. It is just conventional to group all the x terms on the left side of the equation.

The direct answer to your question is this:  The goal is to wind up with an equation with all of the terms with an X in them on the left side, and all of the terms that are just numbers are on the right side of the equals sign.  (As Elizabeth said, it doesn't really matter which is on which side as long as all of the x's and numbers wind up together with only other x's and numbers.)

You want to "move" the 4x from the right side to the left side.  How do you do that?  Just subtract 4x from the right side.  4x minus 4x equals zero, so it goes away.  To keep the equation balanced, you have to subtract the same amount from the left side.  

Similarly, you want to move that -2 to the right side, so you have to add +2 to both sides to make the -2 on the left go away.  When you get them all sorted out on the correct sides of the equation, you can add up the X terms on one side and the numbers on the other side.

At that point you had 4x = 8.  We want to know what X is, so we need to make the 4 go away.  To do that, you have to divide by 4 (both sides again!).  4 divided by 4 is 1, so the 4 disappears on the left (4x becomes just x) and you wind up with your answer:

x = 2

I hope this will help clear it up for you.

Hi Anthony,

 

Technically, you could have done it either way.  Here's what you had:

-2 + 8x = 6 + 4x

Then you subtracted 4x from both sides and combined like terms:

-2 + 8x - 4x = 6 + 4x - 4x

-2 + 4x = 6

And then you added 2 to both sides and divided by 4 to isolate the variable x:

4x = 8

x = 2

 

However, you could have done it by subtracting the 8x from both sides instead:

-2 + 8x - 8x = 6 + 4x - 8x

-2 = 6 - 4x

And then you would have to subtract 6 from both sides and divide by negative 4:

-8 = -4x

2 = x

 

Either way, you come to the same answer.  The reason your given solution decided to subtract the 4x was so that you wouldn't have to deal with negative numbers because sometimes the changing of signs can confuse people.  But both ways are mathematically correct.

 

Comment

Hello, Anthony:

You may want to remember this rule in a different form:

Any term can be moved from one side to another if you change its sign.

Example: -2 + 8x = 6 + 4x

If I want to move 4x to the left, all I do is change its sign from + to - and write it on the left side. That is,

-2 + 8x = 6 + 4x goes into -2 + 8x - 4x =6. Why moving? In order to combine like terms on one side. Terms containing x are usually combined on the left, whereas numbers are combined on the right (although you can do it oppositely--there is nothing wrong with that!). So, we have now -2 + 8x - 4x =6. We now need to move -2 to the right. Try to move it according to the rule I just gave and then scroll down to check your answer.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The answer is 8x -4x= 6 + 2. We simply took -2 from the left, changed its sign to +2 and added it to the right side. Now the rest shall be easy: combine like terms to get 4x=8 and then divide both parts by 4 to get x=2.

Hope it got clearer.

Hi Anthony,

The reason we add a number to each side of an equation is:

  1. Whatever you do to one side of an equation you must do the other side of the equation.
  2. Adding numbers to each side of an equation is how we are able to move terms from one side of the equation to the other. 

Therefore:

  • -2 + 8x = 6 + 4x Looking at the equation we know that we have one term containing x on the right that needs to be moved to the left (4x) and then we have one other term on the left that needs to be moved to the right (-2). 
  • To remove the 4x from the right side of the equation we would need to subtract it from itself, because any positive number subtracted from itself is zero. Therefore we would add -4x to the right side of the equation and then as mentioned above, anything we do to one side of an equation we have to do the same thing to the other side. So we would have:
    1. -2 + 8x -4x = 6 + 4x - 4x
    2. = -2 + 8x - 4x = 6 + 0
    3. = -2 + 8x - 4x = 6
  • Now looking at the equation we still have another term on the left side of the equation that needs to be moved to the right side (-2). In order to remove the -2 from the left side we will need to add it to itself because any negative number added to itself is zero. Therefore we would add 2 to the left side of the equation and then also add 2 to the right side because anything we do to one side of an equation we have to do the same thing to the other side as well. 
    1. ==> -2 + 2 + 8x - 4x = 6 + 2
    2. = 0 + 8x - 4x = 6 + 2
    3. 8x - 4x = 6 + 2

Looking over the equation now you see that we have all like terms on the same side of the equation in order for you to solve for x. 

Hope this helped!


   6x – 2 + 2x = - 2 + 4x + 8
       + 2          + 2  
          0             0

   6x + 2x = 4x + 8
 - 4x         - 4x  
  2x            0 

   2x + 2x = 8
(2 apples and 2 apples are 4 apples, same with "x": 2x and 2x are 4x)

    4x  =  8
÷ 4     ÷ 4

   x = 2 

Check the answer (in original equation substitute "x" by "2" )
6 • 2 – 2 + 2 • 2 = - 2 + 4 • 2 + 8
  12  – 2 +   4    = - 2 +    8   + 8
                   14 = 14