Question

modulus X + 7 + modulus 5 minus x is equal to 12​

Answer 1

Answer:

Solution :

71 - x = 8n

71 - x is the multiple of 8

if x = 1, 71 - x = 70 is not the multiple of 8,

The number which is nearest to 71 is 64 (multiple of 8).In order to make this 71 as 64, we have to subtract 7.

So, the value of x is 7.

Hence 7 is the least number.

(ii) 78 + x ≡ 3 (mod 5)

Solution :

78 + x = 3 (mod 5)

78 + x - 3 = 5n

75 + x = 5n

If x = 5, then 75 + 5 = 80(which is the multiple of 5)

Hence 5 is the least number.

(iii) 89 ≡ (x + 3) (mod 4)

Solution :

89 = (x + 3) (mod 4)

89 - x - 3 = 4n

86 - x = 4n

If x = 2, then 86 - 2 = 84(which is the multiple of 4)

Hence 2 is the least number.

(iv) 96 ≡ (x/7) (mod 5)

Solution :

96 ≡ (x/7) (mod 5)

By dividing 96 by 5, we get 1 as remainder

1 = x/7

x = 7

Hence the least value of x is 7.

(v) 5x ≡ 4 (mod 6)

Solution :

5x ≡ 4 (mod 6)

5x - 4 = 6n

If x = 2, then 10 - 4 = 6 (which is the multiple of 6)

Hence 2 is the least number.