Question

If x is congruent to 13 modulo 17 then 7x-3 is congruent to which number

Answer 1

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