how many integer solutions does (4n+19)/(n-3) has?

2

4

8

infinte many

Answer: (2) 4 solutions

Solution

(4n-12+31)/(n-3) = 4+31/(n-3)

so now 31/(n-3) let’s say equal to 31/x  should be integer

it will be integer when x is a factor of 31 (both positive and negative)

there are 2 positive factors of 31 and 2 negative factors. Hence total 4 solutions.

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