3(x + 2) - 4 = 8x + 2 [Is x 0 or undefined??]

[niknatdad]

There seem to be 2 ways to solve this equation. Which way is correct? Why?

Solve for x:
3(x + 2) - 4 = 8x + 2

My solution:

3(x + 2) - 4 = 8x + 2
3x + 6 - 4 = 8x + 2
3x + 2 = 8x + 2
3x <> 8x [3x does not equal 8x]
undefined

**OR**

3(x + 2) - 4 = 8x + 2
3x + 6 - 4 = 8x + 2
3x + 2 = 8x + 2
2 = 5x + 2
0 = 5x
x = 0/5
x=0

But what is the rule that indicates one way over the other?

Any help would be great.

Thanks

 

[skeeter]

3x = 8x

3x - 3x = 8x - 3x

0 = 5x

0 = x

x = 0 is the only solution.

 

[tkhunny]

3x <> 8x

This is an interesting conclusion, but it is the result of asking not quite the right question. Rather than asking yourself, "Are they equal?" ask "Is there a value for 'x' that will make them equal?" This question should lead you to x = 0.

 

[niknatdad]

I see my mistake now. As always, they seem so simpleminded in hindsight.

Thanks for the help tkhunny.