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It has been twenty-plus years since I graduated high school and completed any type of math courses through a higher education institution.  Therefore, could you please refresh my memory for the reason(s) why one determines which side to add or subtract from a certain side when solving linear equations?  For example: 2(x-8)+8x=4x+6(x-3)                                            2x-16+8x=4x+6x-18                                            10x-16=10x-18 (here is where my question comes into play - why subtract 16 from 18 and not the other way around)

Question

It has been twenty-plus years since I graduated high school and completed any type of math courses through a higher education institution.  Therefore, could you please refresh my memory for the reason(s) why one determines which side to add or subtract from a certain side when solving linear equations?  For example: 2(x-8)+8x=4x+6(x-3) 

                                           2x-16+8x=4x+6x-18

                                            10x-16=10x-18 (here is where my question comes into play - why subtract 16 from 18 and not the other way around)

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Step 1

First of all, you took the wrong example of linear equation, because here 10x will be cancelled out and then 16=18, which is absurd.

So, take the equation as:

2(x-8)+8x 3x+ 6(x-3)
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2(x-8)+8x 3x+ 6(x-3)

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Step 2

Now, further sim...

10x
16 9x -18
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10x 16 9x -18

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