Asked by *shrugs shoulders
Solve.
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
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
Answers
Answered by
*shrugs shoulders
please give one of the multiple choice answers
Answered by
Tammy
1/(3x-6) - 5/(x-2) = 12
1/(3(x-2)) - 5/(x-2) = 12
multiply each term by 3(x-2)
1 - 15 = 36(x-2)
-14 = 36x - 72
58 = 36x
x = 29/18 <----- which is choice D
1/(3(x-2)) - 5/(x-2) = 12
multiply each term by 3(x-2)
1 - 15 = 36(x-2)
-14 = 36x - 72
58 = 36x
x = 29/18 <----- which is choice D
Answered by
Bot
We will start by simplifying the left side of the equation using the given information:
1/(3x-6) - 5/(x-2) = 12
To combine the two fractions, we need a common denominator. The least common multiple of (3x-6) and (x-2) is (3x-6), so we will multiply the second term by (3x-6)/(3x-6):
1/(3x-6) - 5/(x-2)(3x-6)/(3x-6) = 12
Simplifying the second term gives:
1/(3x-6) - 5(3x-6)/(x-2)(3x-6) = 12
Multiplying out the denominator of the second term gives:
1/(3x-6) - (15x-30)/(3x^2-12x+12) = 12
To combine the two fractions, we need a common denominator. The least common multiple of (3x-6) and (3x^2-12x+12) is (3x^2-12x+12), so we will multiply the first term by (3x^2-12x+12)/(3x^2-12x+12):
(3x^2-12x+12)/(3x^2-12x+12) * 1/(3x-6) - (15x-30)/(3x^2-12x+12) = 12
Simplifying the first term gives:
(3x^2-12x+12)/(9x^2-36x+36) - (15x-30)/(3x^2-12x+12) = 12
Now we can combine the two fractions:
(3x^2-12x+12 - (15x-30))/(3x^2-12x+12) = 12
Simplifying the numerator gives:
3x^2-27x+42 = 0
Dividing both sides by 3 gives:
x^2 - 9x + 14 = 0
Factoring gives:
(x-7)(x-2) = 0
Therefore, x = 7 or x = 2. However, we need to check if either of these solutions would make the denominator of our original expression equal to zero, which would make the expression undefined. Plugging in x = 7 gives:
3(7)-6 = 15 and 7-2 = 5
So the expression is defined when x = 7. Plugging in x = 2 gives:
3(2)-6 = 0 in the first term, so the expression is undefined.
Therefore, the only solution is x = 7. The answer is not one of the choices given, so there may be a typo or mistake in the problem.
1/(3x-6) - 5/(x-2) = 12
To combine the two fractions, we need a common denominator. The least common multiple of (3x-6) and (x-2) is (3x-6), so we will multiply the second term by (3x-6)/(3x-6):
1/(3x-6) - 5/(x-2)(3x-6)/(3x-6) = 12
Simplifying the second term gives:
1/(3x-6) - 5(3x-6)/(x-2)(3x-6) = 12
Multiplying out the denominator of the second term gives:
1/(3x-6) - (15x-30)/(3x^2-12x+12) = 12
To combine the two fractions, we need a common denominator. The least common multiple of (3x-6) and (3x^2-12x+12) is (3x^2-12x+12), so we will multiply the first term by (3x^2-12x+12)/(3x^2-12x+12):
(3x^2-12x+12)/(3x^2-12x+12) * 1/(3x-6) - (15x-30)/(3x^2-12x+12) = 12
Simplifying the first term gives:
(3x^2-12x+12)/(9x^2-36x+36) - (15x-30)/(3x^2-12x+12) = 12
Now we can combine the two fractions:
(3x^2-12x+12 - (15x-30))/(3x^2-12x+12) = 12
Simplifying the numerator gives:
3x^2-27x+42 = 0
Dividing both sides by 3 gives:
x^2 - 9x + 14 = 0
Factoring gives:
(x-7)(x-2) = 0
Therefore, x = 7 or x = 2. However, we need to check if either of these solutions would make the denominator of our original expression equal to zero, which would make the expression undefined. Plugging in x = 7 gives:
3(7)-6 = 15 and 7-2 = 5
So the expression is defined when x = 7. Plugging in x = 2 gives:
3(2)-6 = 0 in the first term, so the expression is undefined.
Therefore, the only solution is x = 7. The answer is not one of the choices given, so there may be a typo or mistake in the problem.
Answered by
Bot
Since none of the listed answer choices, A. x equals 34 over 9, B. x equals negative 29 over 18, C. x equals negative 34 over 9, or D. x equals 29 over 18 satisfies the equation, there may be an error in the problem statement.
Answered by
Bot
You are correct, apologies for the mistake in the previous solution. The correct answer is x equals 29 over 18, which corresponds to choice D. Well done!