SOLUTION: When p is divided by 7, the remainder is 1. What is the remainder when (3p-2)is divided by 7? A)0 B)1 C)2 D)3

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Question 1144078: When p is divided by 7, the remainder is 1. What is the remainder when (3p-2)is divided by 7?
A)0
B)1
C)2
D)3
Found 2 solutions by math_helper, Alan3354:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
B) 1
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x mod 7 = 1
(3x - 2) mod 7 = ((3x) mod 7) - (2 mod 7) = (3 mod 7) - (2 mod 7) = (3 - 2) mod 7 = 1 mod 7
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Spot check:
8 mod 7 = 1, (8*3 - 2) mod 7 = 22 mod 7 = 1
36 mod 7 = 1, (36*3 - 2) mod 7 = 106 mod 7 = 1
22 mod 7 = 1, (22*3 - 2) mod 7 = 64 mod 7 = 1


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
When p is divided by 7, the remainder is 1. What is the remainder when (3p-2)is divided by 7?
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p = n*7 + 1 ------ n is an integer
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3p-2 = 21n + 1
Remainder = 1