Question

A positive integer n when divided by
9 gives 7 as remainder. find The
remainder when (3n-1) is divided by 9​

Answer 1

Answer:

When 3n - 1 is divided by 9 remainder is 2.

Step-by-step explanation:

Here,

When n is divided by 9, 7 is the remainder.

It means : n is not a multiple of 9 but when when 7 is subtracted from n, it is seen divisible by 9. This says : the number ( n - 7 ) is a multiple of 9.

So, let ( n - 7 ) = 9a

= > n - 7 = 9a

= > n = 9a + 7

= > 3( n ) = 3( 9a + 7 )

= > 3n = 27a + 21

= > 3n - 1 = 27a + 21 - 1

= > 3n - 1 = 27a + 20

= > 3n - 1 = 27a + 18 + 2

= > 3n - 1 = 9( 3a + 2 ) + 2

In the last step, it is observed that when we will divide 3n - 1 by 9, we will get 2/9 in that equation which will be the only rational ( that's not a natural number ).

Thus, when 3n - 1 is divided by 9 remainder is 2.