The quotient 1 over the quantity 3 times x minus 6 minus the quotient 5 over the quantity x minus 2 equals 12
A. x equals 34 over 9
B. x equals negative 29 over 18
C. x equals negative 34 over 9
D. x equals 29 over 18
AAAaannndd the bot gets it wrong yet again!
Why do you keep making mistakes on such simple math? You say you are an AI construct, but you seem incapable of actually learning anything!
1/(3x - 6) - 5/(x - 2) = 12
(x-2) - 5(3x-6) = 12(3x-6)(x-2)
36x^2 - 130x + 116 = 0
2(x-2)(18x-29) = 0
x = 2 or 29/18
But x=2 is excluded from the original equation, so the only solution is
D: x = 29/18
I apologize for the mistake in my previous response. You are correct that the correct answer is D: x = 29/18. Thank you for providing the correct solution. As an AI language model, I strive to improve my accuracy and learn from my mistakes.
To solve this equation step-by-step, we will start by simplifying each quotient.
1. Simplify the first quotient: 1 / (3x - 6).
2. Simplify the second quotient: 5 / (x - 2).
The equation then becomes:
1 / (3x - 6) - 5 / (x - 2) = 12.
Now, let's find a common denominator to combine the two fractions on the left-hand side.
3. The common denominator for (3x - 6) and (x - 2) is (3x - 6)(x - 2).
To eliminate the denominators, we multiply the entire equation by this common denominator.
So, we have:
[(3x - 6)(x - 2)] * [1 / (3x - 6)] - [(3x - 6)(x - 2)] * [5 / (x - 2)] = 12 * [(3x - 6)(x - 2)].
4. Simplify each term by canceling out common factors:
(x - 2) - 5(3x - 6) = 12(3x - 6)(x - 2).
Let's continue to simplify further:
x - 2 - 15x + 30 = 36x - 72.
Combine like terms:
-14x + 28 = 36x - 72.
5. Move all the variables to one side and the constants to the other side of the equation:
-14x - 36x = -72 - 28.
-50x = -100.
6. Divide both sides of the equation by -50:
x = (-100) / (-50).
Simplify further:
x = 2.
So, the correct answer is:
A. x equals 34 over 9.
We start by simplifying each of the quotients on the left side of the equation:
1/(3x - 6) = 1/3(x - 2)
5/(x - 2) = 5/(x - 2)
Now we can rewrite the equation as:
1/3(x - 2) - 5/(x - 2) = 12
To combine the fractions, we need a common denominator, which is (x - 2)(3). So we have:
(1/3)(x - 2)(3)/(x - 2) - (5)/(x - 2)(3) = 12
Simplifying the numerators and combining like terms, we get:
x/3 - 5/3 = 12
Adding 5/3 to both sides, we have:
x/3 = 41/3
Multiplying both sides by 3, we get:
x = 41
Therefore, the answer is not listed.