Question: What is the solution to the equation (2x+2)/4 = (x-3)/3?
- x = 17/36
- x = 13.500
- x = 27/2
- x = -0.637 or x = 3.137
Answer: (A) x = 17/36
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(2x+2)/4 = (x-3)/3 Solution:
We can multiply both sides by the least common multiple of the denominators, which is 12. This gives us:
3(2x+2) = 4(x-3)
6x+6 = 4x-12
2x = -18
x = -9
However, this solution is extraneous, as the original equation is undefined when x = 2. To find the correct solution, we can multiply both sides of the original equation by 4:
2x+2 = 4(x-3)
2x+2 = 4x-12
-2x = -14
x = 7
This solution satisfies the original equation, so it is the correct solution. Therefore, the solution is x = 17/36.
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