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

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

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

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

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

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.

The statement a ≡ b (mod m) means that the difference a - b is divisible by m.

The multiplicative inverse of 3 mod 11 is 4, since (3 * 4) mod 11 = 12 mod 11 = 1.

All operations (addition, subtraction, multiplication) are valid in modular arithmetic.

8 ≡ 15 (mod 8) is false; the correct answer is 5 ≡ 10 (mod 5) is true.

Modular arithmetic is commutative for addition and multiplication, hence non-commutativity is not a property.

Modular arithmetic is primarily applicable to integers, making the first statement true.