If 3x$^o$ 4(mod 5), find the least value of x

The question most likely reads: 3x ≡ 4 (mod 5), and we want the least positive value of x. (The "o" is probably a typing glitch from the congruence symbol.)

Concept

3x ≡ 4 (mod 5) means 3x − 4 is exactly divisible by 5, so 3x leaves a remainder of 4 when divided by 5.

Solution

Test each option:

• x = 1: 3(1) = 3, and 3 mod 5 = 3. This is not 4.
• x = 2: 3(2) = 6, and 6 mod 5 = 1. This is not 4.
• x = 3: 3(3) = 9, and 9 mod 5 = 4. This works.
• x = 4: 3(4) = 12, and 12 mod 5 = 2. This is not 4.

Check by the inverse method

The inverse of 3 mod 5 is 2, because 3 × 2 = 6 ≡ 1 (mod 5). Multiply both sides by 2:

x ≡ 4 × 2 = 8 ≡ 3 (mod 5)

So the least value is x = 3.

Answer: C

Tip: For small moduli, just substitute the options one by one. It's fast and reliable. Also, when you see "least value" in modular arithmetic, you're looking for the smallest positive number that satisfies the congruence.