six less than three times a number is the same as six more than the number. find the number.  

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(x-6) * 3 = x+6Once you distribute the 3, you get 3x-6 = x+6.Subtract the x from both sides, and you get 2x-6=6add 6 to both sides, and you get 2x = 12Simplify the rest, and you get x = 6. Plug in the answer to make sure it works, and voila! You're done :D