15 mod 6 = 3, so x = 3.

Dividing both sides by 2 gives x ≡ 2 (mod 3), hence the smallest non-negative solution is 2.

Dividing both sides by 3 gives x ≡ 3 (mod 12), which means x can be 3.

3x = 9 mod 6 simplifies to x = 3 mod 2, so x = 2.

The multiplicative inverse of 4 mod 9 is 7, since 4 * 7 = 28 ≡ 1 (mod 9).

Dividing both sides by 4 gives x ≡ 2 (mod 3), so the smallest non-negative solution is 2.

Dividing the equation by 4 gives x ≡ 2 (mod 3). The smallest non-negative solution is x = 2.

Dividing both sides by 5 gives x ≡ 2 (mod 3), which means x can be 2.

To solve 7x ≡ 3 (mod 5), we first reduce 7 mod 5 to get 2x ≡ 3 (mod 5). The solution is x ≡ 4 (mod 5), which corresponds to 2.

Dividing both sides by 4 gives 2x ≡ 1 (mod 3). The solution is x = 2.

A number congruent to 0 mod 6 must be a multiple of 6. 12 is a multiple of 6.

x = 5 + 8k for some integer k. 13 is 5 + 8(1), so it is congruent to 5 modulo 8.

a * b ≡ 2 * 1 ≡ 2 (mod 3).

a * b ≡ 2 * 3 ≡ 6 (mod 5), which is equivalent to 1.

a + b ≡ 3 + 5 ≡ 8 ≡ 1 (mod 7).

All operations (addition, multiplication, and subtraction) preserve congruence in modular arithmetic.

All operations (addition, subtraction, multiplication) maintain congruence under modular arithmetic.

x + y ≡ 2 + 1 ≡ 3 (mod 3), which is equivalent to 0, but since we are looking for the value, it is 0 mod 3.

Using the method of successive substitutions or the Chinese Remainder Theorem, the smallest solution is x = 26.

x can be expressed as 4 + 5k, where k is an integer. 19 is not congruent to 4 modulo 5.

10 mod 6 = 4, so x could be 10.

Using the method of successive substitutions or the Chinese Remainder Theorem, we find that the smallest positive integer solution is x = 25.

x + y ≡ 4 + 3 ≡ 7 (mod 7), which is equivalent to 0.

11 mod 7 = 4, so x could be 11.

In modular arithmetic, if a ≡ b (mod m), then (a - b) is divisible by m. Here, 7 - 3 = 4, which is divisible by 4.

Since 7 - 3 = 4, n must be a divisor of 4. Therefore, n can be 1, 2, or 4, but for the congruence to hold, n must be greater than 4.

In modular arithmetic with a modulus of 12 (for hours), 9 + 15 = 24, and 24 mod 12 = 0, which corresponds to 12 o'clock.

In a 12-hour clock, 3 + 10 = 13, and 13 mod 12 = 1.

15 hours from 9 o'clock is calculated as (9 + 15) mod 12 = 24 mod 12 = 0, which is 12 o'clock.

To find x, we calculate 7 mod 5, which is 2. Therefore, x = 2.