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

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(20056) (Show Source): You can put this solution on YOUR website!
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 



Replace x by 7y - 3



Add 3 to all 3 sides



Divide all three sides by 7





Since y is an integer,



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

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