Question

If x and y are real numbers, and 2\sqrt{x-4}-2 = 1, and

|y-5|< 2, what is the smallest possible integer value of x+y?
(A) 9
(B) 10
(C) 11
(D) 12​

Answer 1

Answer: The smallest integer is 10

Step-by-step explanation:

2\sqrt{x-4}-2 = 1 from here x=25/4 or as a mixed fraction 6 1/4.

|y-5|< 2 we get y-5<2 or y-5>-2 and y=7 and y=3.

Since we want an integer we want to see a number greater than 3 that when added to x can make 25/4 an integer. Since 25/4= 6 1/4 then we need a 3/4. 3 3/4+ 6 1/4 gives us 10.

Answer 2

10 is the smallest integer