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Algebra Level 3

If − 2 < y < 3 -2 < y < 3 , then which of the following is true:

9 < ( y − 2 ) 2 < 16 9 < (y-2)^2 < 16 0 ≤ ( y − 2 ) 2 < 16 0 \leq (y-2)^2 < 16 1 < ( y − 2 ) 2 < 16 1 < (y-2)^2 < 16 0 < ( y − 2 ) 2 < 16 0 < (y-2)^2 < 16

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Sarah Maisarah by Sarah Maisarah , 25, Indonesia

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1 solution

Julia Zibordi
Dec 26, 2018

If y y is greater than -2 but smaller than 3, then y y can be -1, 0, 1 or 2. If you try each one of these possibilities in ( y − 2 ) 2 (y-2)^{2} , you'll see that ( − 1 − 2 ) 2 (-1-2)^{2} = 9, ( 0 − 2 ) 2 = 4 (0-2)^{2} = 4 , ( 1 − 2 ) 2 = 1 (1-2)^{2} = 1 and ( 2 − 2 ) 2 (2-2)^{2} = 0. So the only possible answer is the third option. I'm sorry for any typos, I really hope I could help you understand this problem.

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