SOLUTION: The solution of x+5=2(MOD7) and x is an integer between 1 and 12,then how many values does x have

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Question 407951: The solution of x+5=2(MOD7) and x is an integer between 1 and 12,then how many values does x have
Answer by Edwin McCravy(20055) About Me  (Show Source):
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The solution of x+5=2(MOD7) and x is an integer between 1 and 12,then how many values does x have

x + 5 = 2(mod 7)

Replace 2(mod 7) by 7y + 2

x + 5 = 7y + 2

x = 7y - 3

Since 

1+%3C=+x+%3C=+12

Replace x by 7y - 3

1+%3C=+7y+-+3+%3C=+12

Add 3 to all 3 sides

4+%3C=+7y+%3C=+15

Divide all three sides by 7

4%2F7%3C=y%3C=15%2F7

4%2F7%3C=y%3C=2%261%2F7

Since y is an integer,

1%3C=y%3C=2

So either y = 1 or y = 2

Two solutions. 

When y = 1, x = 7y - 3 = 7(1) - 3 = 4
When y = 2, x = 7y - 3 = 7(2) - 3 = 14 - 3 = 11

Edwin