If 6 times some number is decreased by 6, then 3 times some number is increased by 12 what is the number?

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your "then" doesn't help much. I'll just take that as an addition sign. From what you're saying, it goes like:6x - 6 + 3x + 12 = 9x +6 => 9x = -6 => x = -6/9 => x = -2/3. Your answer is -2/3, assuming the two "some numbers" there are in the same problem and not different.If they're separated, it's6x - 6 = 0 => 6x = 6 => x = 1.then 3x + 12 = 0 => 3 x = - 12 => x = -4.There you go, pal.