Question

13.If z is congruent to 10 modulo 17 then 7x – 3 is congruent to which number modulo 17? answer prprly....r else i will report it

Answer 1

Answer:

7x - 3 is congruent to 3 at modulo 17

Or

7x - 3 = 3 (mod 17)

Step-by-step explanation:

Complete question:

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

Solution:

We are going to use properties of congruences

Since

x = 13 (mod 17)   ......(1)

and

7 = 7 (mod 17)     .......(2)

Multiplying congruence (1) and (2) we get

7x = 13 × 7 (mod 17)

7x = 91 (mod 17)       .......(3)

And

91 = 6 (mod 17)      ........(4)

Putting congruence (4) in (3) we get

7x = 6 (mod 17)      .......(5)

Since

3 = 3 (mod 17)    ........(6)

Subtracting congruence (6) from (5) we get

7x - 3 = 6 -3 (mod 17)

7x - 3 = 3 (mod 17)

Thus

7x - 3 is congruent to 3 at modulo 17