If x is congruent to 13 modulo 17 then 7x-3 is congruent to which number
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Answer:
7x-3 is congruent to 3 modulo 17
Step-by-step explanation:
If x is congruent to 13 modulo 17 then 7x-3 is congruent to which number
x is congruent to 13 modulo 17
=> x = 17y + 13 ( y being an integer)
7x-3 = 7(17y + 13) - 3
=> 7x-3 = 7*17y + 91 - 3
=> 7x-3 = 7*17y + 88
=> 7x-3 = 7* 17 y + 85 + 3
=>7x-3 = 7* 17 y + 17*5 + 3
=>7x-3 = 17(7y + 5) + 3
7y + 5 is an integer as y is an integer
hence 7x-3 is congruent to 3 modulo 17
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