20. If 7x=6 mod 5. Then the value of x is: A. 2 B. 3 C. 4 D. 5

To solve this problem, we need to find the value of x that satisfies the given congruence equation.<br /><br />The congruence equation states that 7x is congruent to 6 modulo 5. This means that when 7x is divided by 5, the remainder is 6.<br /><br />To find the value of x, we can use the properties of modular arithmetic. Specifically, we can use the fact that if a ≡ b (mod m), then a ≡ b + km (mod m) for any integer k.<br /><br />In this case, we can rewrite the congruence equation as:<br /><br />7x ≡ 6 (mod 5)<br /><br />To isolate x, we can multiply both sides of the equation by the modular inverse of 7 modulo 5. The modular inverse of 7 modulo 5 is 3, since 7 * 3 ≡ 1 (mod 5).<br /><br />Multiplying both sides of the equation by 3, we get:<br /><br />(3 * 7)x ≡ (3 * 6) (mod 5)<br /><br />Simplifying, we have:<br /><br />21x ≡ 18 (mod 5)<br /><br />Since 21 ≡ 1 (mod 5) and 18 ≡ mod 5), we can rewrite the equation as:<br /><br />x ≡ 3 (mod 5)<br /><br />This means that x is congruent to 3 modulo 5, which implies that x = 5k + 3 for some integer k.<br /><br />Therefore, the correct answer is B. 3.