Anthony D.

asked • 08/13/13

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.

4 Answers By Expert Tutors

By:

Elizabeth S. answered • 08/13/13

Tutor
4.9 (117)

Middle School/High School/College Mathematics Tutor

Anthony D.

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

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08/13/13

Christopher G.

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.

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08/13/13

Gene G.

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.

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08/13/13

Joya A.

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.

 

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08/13/13

Nataliya D. answered • 08/13/13

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Efe M. answered • 08/13/13

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